{"id":46,"date":"2017-10-27T16:28:44","date_gmt":"2017-10-27T16:28:44","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/chapter\/physical-quantities-and-units\/"},"modified":"2017-11-08T03:23:39","modified_gmt":"2017-11-08T03:23:39","slug":"physical-quantities-and-units","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/chapter\/physical-quantities-and-units\/","title":{"raw":"Physical Quantities and Units","rendered":"Physical Quantities and Units"},"content":{"raw":"\n<div class=\"textbox learning-objectives\">\n<h3 itemprop=\"educationalUse\">Learning Objectives<\/h3>\n<ul>\n<li>Perform unit conversions both in the SI and English units.\n<\/li>\n<li>Explain the most common prefixes in the SI units and be able to write them in scientific notation.<\/li>\n<\/ul>\n<\/div>\n<div class=\"bc-figure figure\" id=\"import-auto-id2657097\">\n<div class=\"bc-figcaption figcaption\">The distance from Earth to the Moon may seem immense, but it is just a tiny fraction of the distances from Earth to other celestial bodies. (credit: NASA)<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id3164906\" data-alt=\"A view of Earth from the Moon.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_01_02_01b.jpg\" data-media-type=\"image\/png\" alt=\"A view of Earth from the Moon.\" width=\"300\"><\/span><\/p><\/div>\n<p id=\"import-auto-id2510075\">The range of objects and phenomena studied in physics is immense. From the incredibly short lifetime of a nucleus to the age of the Earth, from the tiny sizes of sub-nuclear particles to the vast distance to the edges of the known universe, from the force exerted by a jumping flea to the force between Earth and the Sun, there are enough factors of 10 to challenge the imagination of even the most experienced scientist. Giving numerical values for physical quantities and equations for physical principles allows us to understand nature much more deeply than does qualitative description alone. To comprehend these vast ranges, we must also have accepted units in which to express them. And we shall find that (even in the potentially mundane discussion of meters, kilograms, and seconds) a profound simplicity of nature appears\u2014all physical quantities can be expressed as combinations of only four fundamental physical quantities: length, mass, time, and electric current.<\/p>\n<p id=\"import-auto-id1675918\">We define a <span data-type=\"term\" id=\"import-auto-id1536256\">physical quantity<\/span> either by  <em data-effect=\"italics\">specifying how it is measured<\/em> or by <em data-effect=\"italics\"><em data-effect=\"italics\">stating how it is calculated<\/em><\/em> from other measurements. For example, we define distance and time by specifying methods for measuring them, whereas we define <em data-effect=\"italics\"><em data-effect=\"italics\">average speed<\/em><\/em> by stating that it is calculated as distance traveled divided by time of travel.<\/p>\n<p id=\"import-auto-id2985261\">Measurements of physical quantities are expressed in terms of <span data-type=\"term\" id=\"import-auto-id1666000\">units<\/span>, which are standardized values. For example, the length of a race, which is a physical quantity, can be expressed in units of meters (for sprinters) or kilometers (for distance runners). Without standardized units, it would be extremely difficult for scientists to express and compare measured values in a meaningful way. (See <a href=\"#import-auto-id2991258\" class=\"autogenerated-content\">(Figure)<\/a>.)<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id2991258\">\n<div class=\"bc-figcaption figcaption\">Distances given in unknown units are maddeningly useless.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id2750660\" data-alt=\"A boy looking at a map and trying to guess distances with unit of length mentioned as cables between two points.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_01_02_01a.jpg\" data-media-type=\"image\/jpg\" alt=\"A boy looking at a map and trying to guess distances with unit of length mentioned as cables between two points.\" height=\"225\"><\/span><\/p><\/div>\n<p id=\"import-auto-id1284944\">There are two major systems of units used in the world: <span data-type=\"term\">SI units<\/span> (also known as the metric system) and <span data-type=\"term\">English units<\/span> (also known as the customary or imperial system). <strong>English units<\/strong> were historically used in nations once ruled by the British Empire and are still widely used in the United States. Virtually every other country in the world now uses SI units as the standard; the metric system is also the standard system agreed upon by scientists and mathematicians. The acronym \u201cSI\u201d is derived from the French <em data-effect=\"italics\">Syst\u00e8me International<\/em>.<\/p>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1964667\">\n<h1 data-type=\"title\">SI Units: Fundamental and Derived Units<\/h1>\n<p id=\"import-auto-id2605641\"><a href=\"#import-auto-id3094653\" class=\"autogenerated-content\">(Figure)<\/a> gives the fundamental SI units that are used throughout this textbook. This text uses non-SI units in a few applications where they are in very common use, such as the measurement of blood pressure in millimeters of mercury (mm Hg). Whenever non-SI units are discussed, they will be tied to SI units through conversions.<\/p>\n<table id=\"import-auto-id3094653\" summary=\"A table listing fundamental S I units with two rows. One row lists the physical quantities and the other lists their units.\">\n<caption><span data-type=\"title\">Fundamental SI Units<\/span><\/caption>\n<thead>\n<tr>\n<th><strong>Length<\/strong><\/th>\n<th><strong>Mass<\/strong><\/th>\n<th><strong>Time<\/strong><\/th>\n<th><strong>Electric Current<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>meter (m)<\/td>\n<td>kilogram (kg)<\/td>\n<td>second (s)<\/td>\n<td>ampere (A)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"import-auto-id2729047\">It is an intriguing fact that some physical quantities are more fundamental than others and that the most fundamental physical quantities can be defined <em data-effect=\"italics\"><em data-effect=\"italics\">only<\/em><\/em> in terms of the procedure used to measure them. The units in which they are measured are thus called <span data-type=\"term\" id=\"import-auto-id3097983\">fundamental units<\/span>. In this textbook, the fundamental physical quantities are taken to be length, mass, time, and electric current. (Note that electric current will not be introduced until much later in this text.) All other physical quantities, such as force and electric charge, can be expressed as algebraic combinations of length, mass, time, and current (for example, speed is length divided by time); these units are called <span data-type=\"term\">derived units<\/span>.<\/p>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id3102294\">\n<h1 data-type=\"title\">Units of Time, Length, and Mass: The Second, Meter, and Kilogram<\/h1>\n<div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id2929182\">\n<h2 data-type=\"title\">The Second<\/h2>\n<p id=\"import-auto-id1598785\">The SI unit for time, the <span data-type=\"term\" id=\"import-auto-id2526901\">second<\/span>(abbreviated s), has a long history. For many years it was defined as 1\/86,400 of a mean solar day. More recently, a new standard was adopted to gain greater accuracy and to define the second in terms of a non-varying, or constant, physical phenomenon (because the solar day is getting longer due to very gradual slowing of the Earth\u2019s rotation). Cesium atoms can be made to vibrate in a very steady way, and these vibrations can be readily observed and counted. In 1967 the second was redefined as the time required for 9,192,631,770 of these vibrations. (See <a href=\"#import-auto-id2575847\" class=\"autogenerated-content\">(Figure)<\/a>.) Accuracy in the fundamental units is essential, because all measurements are ultimately expressed in terms of fundamental units and can be no more accurate than are the fundamental units themselves.<\/p>\n<div class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">An atomic clock such as this one uses the vibrations of cesium atoms to keep time to a precision of better than a microsecond per year. The fundamental unit of time, the second, is based on such clocks. This image is looking down from the top of an atomic fountain nearly 30 feet tall! (credit: Steve Jurvetson\/Flickr)<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id1310868\" data-alt=\"A top view of an atomic fountain is shown. It measures time using the vibration of the cesium atom.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_01_02_02a.jpg\" data-media-type=\"image\/jpg\" alt=\"A top view of an atomic fountain is shown. It measures time using the vibration of the cesium atom.\" height=\"225\"><\/span><\/p><\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id2998899\">\n<h2 data-type=\"title\">The Meter<\/h2>\n<p id=\"import-auto-id2837009\">The SI unit for length is the <span data-type=\"term\" id=\"import-auto-id1629056\">meter<\/span> (abbreviated m); its definition has also changed over time to become more accurate and precise. The meter was first defined in 1791 as 1\/10,000,000 of the distance from the equator to the North Pole. This measurement was improved in 1889 by redefining the meter to be the distance between two engraved lines on a platinum-iridium bar now kept near Paris. By 1960, it had become possible to define the meter even more accurately in terms of the wavelength of light, so it was again redefined as 1,650,763.73 wavelengths of orange light emitted by krypton atoms. In 1983, the meter was given its present definition (partly for greater accuracy) as the distance light travels in a vacuum in 1\/299,792,458 of a second. (See <a href=\"#import-auto-id1381492\" class=\"autogenerated-content\">(Figure)<\/a>.) This change defines the speed of light to be exactly 299,792,458 meters per second. The length of the meter will change if the speed of light is someday measured with greater accuracy.<\/p>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id2786029\">\n<h2 data-type=\"title\">The Kilogram<\/h2>\n<p id=\"import-auto-id3204634\">The SI unit for mass is the <span data-type=\"term\" id=\"import-auto-id1989656\">kilogram<\/span> (abbreviated kg); it is defined to be the mass of a platinum-iridium cylinder kept with the old meter standard at the International Bureau of Weights and Measures near Paris. Exact replicas of the standard kilogram are also kept at the United States\u2019 National Institute of Standards and Technology, or NIST, located in Gaithersburg, Maryland outside of Washington D.C., and at other locations around the world. The determination of all other masses can be ultimately traced to a comparison with the standard mass.<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id1381492\">\n<div class=\"bc-figcaption figcaption\">The meter is defined to be the distance light travels in 1\/299,792,458 of a second in a vacuum. Distance traveled is speed multiplied by time.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id2509382\" data-alt=\"Beam of light from a flashlight is represented by an arrow pointing right, traveling the length of a meter stick.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_01_02_03a.jpg\" data-media-type=\"image\/jpg\" alt=\"Beam of light from a flashlight is represented by an arrow pointing right, traveling the length of a meter stick.\" width=\"400\"><\/span><\/p><\/div>\n<p id=\"import-auto-id1255984\">Electric current and its accompanying unit, the ampere, will be introduced in <a href=\"\/contents\/127f63f7-d67f-4710-8625-2b1d4128ef6b@2\">Introduction to Electric Current, Resistance, and Ohm's Law<\/a> when electricity and magnetism are covered. The initial modules in this textbook are concerned with mechanics, fluids, heat, and waves. In these subjects all pertinent physical quantities can be expressed in terms of the fundamental units of length, mass, and time.<\/p>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id2559237\">\n<h1 data-type=\"title\">Metric Prefixes<\/h1>\n<p id=\"import-auto-id2789715\">SI units are part of the <span data-type=\"term\" id=\"import-auto-id2678122\">metric system<\/span>. The metric system is convenient for scientific and engineering calculations because the units are categorized by factors of 10. <a href=\"#import-auto-id2643474\" class=\"autogenerated-content\">(Figure)<\/a> gives metric prefixes and symbols used to denote various factors of 10.<\/p>\n<p id=\"import-auto-id1309728\">Metric systems have the advantage that conversions of units involve only powers of 10. There are 100 centimeters in a meter, 1000 meters in a kilometer, and so on. In nonmetric systems, such as the system of U.S. customary units, the relationships are not as simple\u2014there are 12 inches in a foot, 5280 feet in a mile, and so on. Another advantage of the metric system is that the same unit can be used over extremely large ranges of values simply by using an appropriate metric prefix. For example, distances in meters are suitable in construction, while distances in kilometers are appropriate for air travel, and the tiny measure of nanometers are convenient in optical design. With the metric system there is no need to invent new units for particular applications.<\/p>\n<p id=\"import-auto-id1577727\">The term <span data-type=\"term\" id=\"import-auto-id1363292\">order of magnitude<\/span> refers to the scale of a value expressed in the metric system. Each power of [latex]\\text{10}[\/latex] in the metric system represents a different order of magnitude. For example, [latex]{\\text{10}}^{1},\\phantom{\\rule{0.25em}{0ex}}{\\text{10}}^{2},\\phantom{\\rule{0.25em}{0ex}}{\\text{10}}^{3}[\/latex], and so forth are all different orders of magnitude. All quantities that can be expressed as a product of a specific power of [latex]\\text{10}[\/latex] are said to be of the <em data-effect=\"italics\"><em data-effect=\"italics\">same<\/em><\/em> order of magnitude. For example, the number [latex]\\text{800}[\/latex] can be written as [latex]8\u00d7{\\text{10}}^{2}[\/latex], and the number [latex]\\text{450}[\/latex] can be written as [latex]4.5\u00d7{\\text{10}}^{2}.[\/latex] Thus, the numbers [latex]\\text{800}[\/latex] and [latex]\\text{450}[\/latex] are of the same order of magnitude: [latex]{\\text{10}}^{2}.[\/latex] Order of magnitude can be thought of as a ballpark estimate for the scale of a value. The diameter of an atom is on the order of [latex]{\\text{10}}^{-9}\\text{&nbsp;m,}[\/latex] while the diameter of the Sun is on the order of [latex]{\\text{10}}^{9}\\text{&nbsp;m.}[\/latex]<\/p>\n<div data-type=\"note\" class=\"note\" data-has-label=\"true\" id=\"fs-id2834817\" data-label=\"\">\n<div data-type=\"title\" class=\"title\">The Quest for Microscopic Standards for Basic Units<\/div>\n<p id=\"import-auto-id1113253\">The fundamental units described in this chapter are those that produce the greatest accuracy and precision in measurement. There is a sense among physicists that, because there is an underlying microscopic substructure to matter, it would be most satisfying to base our standards of measurement on microscopic objects and fundamental physical phenomena such as the speed of light. A microscopic standard has been accomplished for the standard of time, which is based on the oscillations of the cesium atom.<\/p>\n<p id=\"import-auto-id2596896\">The standard for length was once based on the wavelength of light (a small-scale length) emitted by a certain type of atom, but it has been supplanted by the more precise measurement of the speed of light. If it becomes possible to measure the mass of atoms or a particular arrangement of atoms such as a silicon sphere to greater precision than the kilogram standard, it may become possible to base mass measurements on the small scale. There are also possibilities that electrical phenomena on the small scale may someday allow us to base a unit of charge on the charge of electrons and protons, but at present current and charge are related to large-scale currents and forces between wires.<\/p>\n<\/div>\n<table id=\"import-auto-id2643474\" summary=\"A table listing metric prefixes for powers of ten and their symbols. The table has the four columns prefix, value, symbol, and example and each row mentions one example.\">\n<caption><span data-type=\"title\">Metric Prefixes for Powers of 10 and their Symbols<\/span><\/caption>\n<thead>\n<tr>\n<th>Prefix<\/th>\n<th>Symbol<\/th>\n<th>Value<a data-type=\"footnote-number\" href=\"#footnote1\"><sup>1<\/sup><\/a><\/th>\n<th colspan=\"4\">Example (some are approximate)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>exa<\/td>\n<td>E<\/td>\n<td>[latex]{\\text{10}}^{\\text{18}}[\/latex]<\/td>\n<td>exameter<\/td>\n<td>Em<\/td>\n<td>[latex]{\\text{10}}^{\\text{18}}\\text{&nbsp;m}[\/latex]<\/td>\n<td>distance light travels in a century<\/td>\n<\/tr>\n<tr>\n<td>peta<\/td>\n<td>P<\/td>\n<td>[latex]{\\text{10}}^{\\text{15}}[\/latex]<\/td>\n<td>petasecond<\/td>\n<td>Ps<\/td>\n<td>[latex]{\\text{10}}^{\\text{15}}\\text{&nbsp;s}[\/latex]<\/td>\n<td>30 million years<\/td>\n<\/tr>\n<tr>\n<td>tera<\/td>\n<td>T<\/td>\n<td>[latex]{\\text{10}}^{\\text{12}}[\/latex]<\/td>\n<td>terawatt<\/td>\n<td>TW<\/td>\n<td>[latex]{\\text{10}}^{\\text{12}}\\text{&nbsp;W}[\/latex]<\/td>\n<td>powerful laser output<\/td>\n<\/tr>\n<tr>\n<td>giga<\/td>\n<td>G<\/td>\n<td>[latex]{\\text{10}}^{9}[\/latex]<\/td>\n<td>gigahertz<\/td>\n<td>GHz<\/td>\n<td>[latex]{\\text{10}}^{9}\\text{&nbsp;Hz}[\/latex]<\/td>\n<td>a microwave frequency<\/td>\n<\/tr>\n<tr>\n<td>mega<\/td>\n<td>M<\/td>\n<td>[latex]{\\text{10}}^{6}[\/latex]<\/td>\n<td>megacurie<\/td>\n<td>MCi<\/td>\n<td>[latex]{\\text{10}}^{6}\\text{&nbsp;Ci}[\/latex]<\/td>\n<td>high radioactivity<\/td>\n<\/tr>\n<tr>\n<td>kilo<\/td>\n<td>k<\/td>\n<td>[latex]{\\text{10}}^{3}[\/latex]<\/td>\n<td>kilometer<\/td>\n<td>km<\/td>\n<td>[latex]{\\text{10}}^{3}\\text{&nbsp;m}[\/latex]<\/td>\n<td>about 6\/10 mile<\/td>\n<\/tr>\n<tr>\n<td>hecto<\/td>\n<td>h<\/td>\n<td>[latex]{\\text{10}}^{2}[\/latex]<\/td>\n<td>hectoliter<\/td>\n<td>hL<\/td>\n<td>[latex]{\\text{10}}^{2}\\text{&nbsp;L}[\/latex]<\/td>\n<td>26 gallons<\/td>\n<\/tr>\n<tr>\n<td>deka<\/td>\n<td>da<\/td>\n<td>[latex]{\\text{10}}^{1}[\/latex]<\/td>\n<td>dekagram<\/td>\n<td>dag<\/td>\n<td>[latex]{\\text{10}}^{1}\\text{&nbsp;g}[\/latex]<\/td>\n<td>teaspoon of butter<\/td>\n<\/tr>\n<tr>\n<td>\u2014<\/td>\n<td>\u2014<\/td>\n<td>[latex]{\\text{10}}^{0}[\/latex] (=1)<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>deci<\/td>\n<td>d<\/td>\n<td>[latex]{\\text{10}}^{-1}[\/latex]<\/td>\n<td>deciliter<\/td>\n<td>dL<\/td>\n<td>[latex]{\\text{10}}^{-1}\\text{&nbsp;L}[\/latex]<\/td>\n<td>less than half a soda<\/td>\n<\/tr>\n<tr>\n<td>centi<\/td>\n<td>c<\/td>\n<td>[latex]{\\text{10}}^{-2}[\/latex]<\/td>\n<td>centimeter<\/td>\n<td>cm<\/td>\n<td>[latex]{\\text{10}}^{-2}\\text{&nbsp;m}[\/latex]<\/td>\n<td>fingertip thickness<\/td>\n<\/tr>\n<tr>\n<td>milli<\/td>\n<td>m<\/td>\n<td>[latex]{\\text{10}}^{-3}[\/latex]<\/td>\n<td>millimeter<\/td>\n<td>mm<\/td>\n<td>[latex]{\\text{10}}^{-3}\\text{&nbsp;m}[\/latex]<\/td>\n<td>flea at its shoulders<\/td>\n<\/tr>\n<tr>\n<td>micro<\/td>\n<td>\u00b5<\/td>\n<td>[latex]{\\text{10}}^{-6}[\/latex]<\/td>\n<td>micrometer<\/td>\n<td>\u00b5m<\/td>\n<td>[latex]{\\text{10}}^{-6}\\text{&nbsp;m}[\/latex]<\/td>\n<td>detail in microscope<\/td>\n<\/tr>\n<tr>\n<td>nano<\/td>\n<td>n<\/td>\n<td>[latex]{\\text{10}}^{-9}[\/latex]<\/td>\n<td>nanogram<\/td>\n<td>ng<\/td>\n<td>[latex]{\\text{10}}^{-9}\\text{&nbsp;g}[\/latex]<\/td>\n<td>small speck of dust<\/td>\n<\/tr>\n<tr>\n<td>pico<\/td>\n<td>p<\/td>\n<td>[latex]{\\text{10}}^{-\\text{12}}[\/latex]<\/td>\n<td>picofarad<\/td>\n<td>pF<\/td>\n<td>[latex]{\\text{10}}^{-\\text{12}}\\text{&nbsp;F}[\/latex]<\/td>\n<td>small capacitor in radio<\/td>\n<\/tr>\n<tr>\n<td>femto<\/td>\n<td>f<\/td>\n<td>[latex]{\\text{10}}^{-\\text{15}}[\/latex]<\/td>\n<td>femtometer<\/td>\n<td>fm<\/td>\n<td>[latex]{\\text{10}}^{-\\text{15}}\\text{&nbsp;m}[\/latex]<\/td>\n<td>size of a proton<\/td>\n<\/tr>\n<tr>\n<td>atto<\/td>\n<td>a<\/td>\n<td>[latex]{\\text{10}}^{-\\text{18}}[\/latex]<\/td>\n<td>attosecond<\/td>\n<td>as<\/td>\n<td>[latex]{\\text{10}}^{-\\text{18}}\\text{&nbsp;s}[\/latex]<\/td>\n<td>time light crosses an atom<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1936382\">\n<h1 data-type=\"title\">Known Ranges of Length, Mass, and Time<\/h1>\n<p id=\"import-auto-id2688624\">The vastness of the universe and the breadth over which physics applies are illustrated by the wide range of examples of known lengths, masses, and times in <a href=\"#import-auto-id1677589\" class=\"autogenerated-content\">(Figure)<\/a>. Examination of this table will give you some feeling for the range of possible topics and numerical values. (See <a href=\"#import-auto-id3143533\" class=\"autogenerated-content\">(Figure)<\/a> and <a href=\"#import-auto-id3083060\" class=\"autogenerated-content\">(Figure)<\/a>.)<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id3143533\">\n<div class=\"bc-figcaption figcaption\">Tiny phytoplankton swims among crystals of ice in the Antarctic Sea. They range from a few micrometers to as much as 2 millimeters in length. (credit: Prof. Gordon T. Taylor, Stony Brook University; NOAA Corps Collections)<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id3440141\" data-alt=\"A magnified image of tiny phytoplankton swimming among the crystal of ice.[\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_01_02_04a.jpg\" data-media-type=\"image\/jpg\" alt=\"A magnified image of tiny phytoplankton swimming among the crystal of ice.[\" width=\"250\"><\/span><\/p><\/div>\n<div class=\"bc-figure figure\" id=\"import-auto-id3083060\">\n<div class=\"bc-figcaption figcaption\">Galaxies collide 2.4 billion light years away from Earth. The tremendous range of observable phenomena in nature challenges the imagination. (credit: NASA\/CXC\/UVic.\/A. Mahdavi et al. Optical\/lensing: CFHT\/UVic.\/H. Hoekstra et al.)<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id2822519\" data-alt=\"A view of Abell Galaxy with some bright stars and some hot gases.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_01_02_05a.jpg\" data-media-type=\"image\/jpg\" alt=\"A view of Abell Galaxy with some bright stars and some hot gases.\" height=\"250\"><\/span><\/p><\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1305702\">\n<h1 data-type=\"title\">Unit Conversion and Dimensional Analysis<\/h1>\n<p id=\"import-auto-id1959437\">It is often necessary to convert from one type of unit to another. For example, if you are reading a European cookbook, some quantities may be expressed in units of liters and you need to convert them to cups. Or, perhaps you are reading walking directions from one location to another and you are interested in how many miles you will be walking. In this case, you will need to convert units of feet to miles.<\/p>\n<p id=\"import-auto-id1430021\">Let us consider a simple example of how to convert units. Let us say that we want to convert 80 meters (m) to kilometers (km).<\/p>\n<p id=\"import-auto-id1595008\">The first thing to do is to list the units that you have and the units that you want to convert to. In this case, we have units in <em data-effect=\"italics\"><em data-effect=\"italics\">meters<\/em><\/em> and we want to convert to <em data-effect=\"italics\"><em data-effect=\"italics\">kilometers<\/em><\/em>.<\/p>\n<p id=\"import-auto-id3083046\">Next, we need to determine a <span data-type=\"term\" id=\"import-auto-id2657858\">conversion factor<\/span> relating meters to kilometers. A conversion factor is a ratio expressing how many of one unit are equal to another unit. For example, there are 12 inches in 1 foot, 100 centimeters in 1 meter, 60 seconds in 1 minute, and so on. In this case, we know that there are 1,000 meters in 1 kilometer.<\/p>\n<p id=\"import-auto-id2675967\">Now we can set up our unit conversion. We will write the units that we have and then multiply them by the conversion factor so that the units cancel out, as shown:<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-442\">[latex]80\\overline{)\\text{m}}\u00d7\\frac{\\text{1 km}}{1000\\overline{)\\text{m}}}=0\\text{.080 km.}[\/latex]<\/div>\n<p id=\"import-auto-id3150430\">Note that the unwanted m unit cancels, leaving only the desired km unit. You can use this method to convert between any types of unit.<\/p>\n<p id=\"import-auto-id2635975\">Click <a href=\"\/contents\/72343285-683e-46d9-a6c2-5de097e36ff9@5\" class=\"autogenerated-content\">(Figure)<\/a> for a more complete list of conversion factors.<\/p>\n<table id=\"import-auto-id1677589\" summary=\"A table is listing approximate values of length, mass, and time with each row containing an example of these.\">\n<caption><span data-type=\"title\">Approximate Values of Length, Mass, and Time<\/span><\/caption>\n<thead>\n<tr>\n<th colspan=\"2\">Lengths in meters<\/th>\n<th colspan=\"2\">Masses in kilograms (more precise values in parentheses)<\/th>\n<th colspan=\"2\">Times in seconds (more precise values in parentheses)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>[latex]{\\text{10}}^{-\\text{18}}[\/latex]<\/td>\n<td>Present experimental limit to smallest observable detail<\/td>\n<td>[latex]{\\text{10}}^{-\\text{30}}[\/latex]<\/td>\n<td>Mass of an electron [latex]\\left(9\\text{.}\\text{11}\u00d7{\\text{10}}^{-\\text{31}}\\phantom{\\rule{0.25em}{0ex}}\\text{&nbsp;kg}\\right)[\/latex]<\/td>\n<td>[latex]{\\text{10}}^{-\\text{23}}[\/latex]<\/td>\n<td>Time for light to cross a proton<\/td>\n<\/tr>\n<tr>\n<td>[latex]{\\text{10}}^{-\\text{15}}[\/latex]<\/td>\n<td>Diameter of a proton<\/td>\n<td>[latex]{\\text{10}}^{-\\text{27}}[\/latex]<\/td>\n<td>Mass of a hydrogen atom [latex]\\left(1\\text{.}\\text{67}\u00d7{\\text{10}}^{-\\text{27}}\\phantom{\\rule{0.25em}{0ex}}\\text{&nbsp;kg}\\right)[\/latex] <\/td>\n<td>[latex]{\\text{10}}^{-\\text{22}}[\/latex]<\/td>\n<td>Mean life of an extremely unstable nucleus<\/td>\n<\/tr>\n<tr>\n<td>[latex]{\\text{10}}^{-\\text{14}}[\/latex]<\/td>\n<td>Diameter of a uranium nucleus<\/td>\n<td>[latex]{\\text{10}}^{-\\text{15}}[\/latex]<\/td>\n<td>Mass of a bacterium<\/td>\n<td>[latex]{\\text{10}}^{-\\text{15}}[\/latex]<\/td>\n<td>Time for one oscillation of visible light<\/td>\n<\/tr>\n<tr>\n<td>[latex]{\\text{10}}^{-\\text{10}}[\/latex]<\/td>\n<td>Diameter of a hydrogen atom<\/td>\n<td>[latex]{\\text{10}}^{-5}[\/latex]<\/td>\n<td>Mass of a mosquito<\/td>\n<td>[latex]{\\text{10}}^{-\\text{13}}[\/latex]<\/td>\n<td>Time for one vibration of an atom in a solid<\/td>\n<\/tr>\n<tr>\n<td>[latex]{\\text{10}}^{-8}[\/latex]<\/td>\n<td>Thickness of membranes in cells of living organisms<\/td>\n<td>[latex]{\\text{10}}^{-2}[\/latex]<\/td>\n<td>Mass of a hummingbird<\/td>\n<td>[latex]{\\text{10}}^{-8}[\/latex]<\/td>\n<td>Time for one oscillation of an FM radio wave<\/td>\n<\/tr>\n<tr>\n<td>[latex]{\\text{10}}^{-6}[\/latex]<\/td>\n<td>Wavelength of visible light<\/td>\n<td>[latex]\\text{1}[\/latex]<\/td>\n<td>Mass of a liter of water (about a quart)<\/td>\n<td>[latex]{\\text{10}}^{-3}[\/latex]<\/td>\n<td>Duration of a nerve impulse<\/td>\n<\/tr>\n<tr>\n<td>[latex]{\\text{10}}^{-3}[\/latex]<\/td>\n<td>Size of a grain of sand<\/td>\n<td>[latex]{\\text{10}}^{2}[\/latex]<\/td>\n<td>Mass of a person<\/td>\n<td>[latex]\\text{1}[\/latex]<\/td>\n<td>Time for one heartbeat<\/td>\n<\/tr>\n<tr>\n<td>[latex]\\text{1}[\/latex]<\/td>\n<td>Height of a 4-year-old child<\/td>\n<td>[latex]{\\text{10}}^{3}[\/latex]<\/td>\n<td>Mass of a car<\/td>\n<td>[latex]{\\text{10}}^{5}[\/latex]<\/td>\n<td>One day [latex]\\left(8\\text{.}\\text{64}\u00d7{\\text{10}}^{4}\\phantom{\\rule{0.25em}{0ex}}\\text{s}\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]{\\text{10}}^{2}[\/latex]<\/td>\n<td>Length of a football field<\/td>\n<td>[latex]{\\text{10}}^{8}[\/latex]<\/td>\n<td>Mass of a large ship <\/td>\n<td>[latex]{\\text{10}}^{7}[\/latex]<\/td>\n<td>One year (y) [latex]\\left(3\\text{.}\\text{16}\u00d7{\\text{10}}^{7}\\phantom{\\rule{0.25em}{0ex}}\\text{s}\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]{\\text{10}}^{4}[\/latex]<\/td>\n<td>Greatest ocean depth<\/td>\n<td>[latex]{\\text{10}}^{\\text{12}}[\/latex]<\/td>\n<td>Mass of a large iceberg<\/td>\n<td>[latex]{\\text{10}}^{9}[\/latex]<\/td>\n<td>About half the life expectancy of a human<\/td>\n<\/tr>\n<tr>\n<td>[latex]{\\text{10}}^{7}[\/latex]<\/td>\n<td>Diameter of the Earth<\/td>\n<td>[latex]{\\text{10}}^{\\text{15}}[\/latex]<\/td>\n<td>Mass of the nucleus of a comet<\/td>\n<td>[latex]{\\text{10}}^{\\text{11}}[\/latex]<\/td>\n<td>Recorded history<\/td>\n<\/tr>\n<tr>\n<td>[latex]{\\text{10}}^{\\text{11}}[\/latex]<\/td>\n<td>Distance from the Earth to the Sun<\/td>\n<td>[latex]{\\text{10}}^{\\text{23}}[\/latex]<\/td>\n<td>Mass of the Moon [latex]\\left(7\\text{.}\\text{35}\u00d7{\\text{10}}^{\\text{22}}\\phantom{\\rule{0.25em}{0ex}}\\text{&nbsp;kg}\\right)[\/latex]<\/td>\n<td>[latex]{\\text{10}}^{\\text{17}}[\/latex]<\/td>\n<td>Age of the Earth<\/td>\n<\/tr>\n<tr>\n<td>[latex]{\\text{10}}^{\\text{16}}[\/latex]<\/td>\n<td>Distance traveled by light in 1 year (a light year)<\/td>\n<td>[latex]{\\text{10}}^{\\text{25}}[\/latex]<\/td>\n<td>Mass of the Earth [latex]\\left(5\\text{.}\\text{97}\u00d7{\\text{10}}^{\\text{24}}\\phantom{\\rule{0.25em}{0ex}}\\text{&nbsp;kg}\\right)[\/latex]<\/td>\n<td>[latex]{\\text{10}}^{\\text{18}}[\/latex]<\/td>\n<td>Age of the universe<\/td>\n<\/tr>\n<tr>\n<td>[latex]{\\text{10}}^{\\text{21}}[\/latex]<\/td>\n<td>Diameter of the Milky Way galaxy<\/td>\n<td>[latex]{\\text{10}}^{\\text{30}}[\/latex]<\/td>\n<td>Mass of the Sun [latex]\\left(1\\text{.}\\text{99}\u00d7{\\text{10}}^{\\text{30}}\\phantom{\\rule{0.25em}{0ex}}\\text{&nbsp;kg}\\right)[\/latex]<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>[latex]{\\text{10}}^{\\text{22}}[\/latex]<\/td>\n<td>Distance from the Earth to the nearest large galaxy (Andromeda)<\/td>\n<td>[latex]{\\text{10}}^{\\text{42}}[\/latex]<\/td>\n<td>Mass of the Milky Way galaxy (current upper limit)<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>[latex]{\\text{10}}^{\\text{26}}[\/latex]<\/td>\n<td>Distance from the Earth to the edges of the known universe<\/td>\n<td>[latex]{\\text{10}}^{\\text{53}}[\/latex]<\/td>\n<td>Mass of the known universe (current upper limit)<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div data-type=\"example\" class=\"textbox examples\" id=\"fs-id2747928\">\n<div data-type=\"title\" class=\"title\">Unit Conversions: A Short Drive Home<\/div>\n<p id=\"import-auto-id3204574\">Suppose that you drive the 10.0 km from your university to home in 20.0 min. Calculate your average speed (a) in kilometers per hour (km\/h) and (b) in meters per second (m\/s). (Note: Average speed is distance traveled divided by time of travel.)<\/p>\n<p id=\"import-auto-id2636340\"><strong>Strategy<\/strong><\/p>\n<p id=\"import-auto-id1951954\">First we calculate the average speed using the given units. Then we can get the average speed into the desired units by picking the correct conversion factor and multiplying by it. The correct conversion factor is the one that cancels the unwanted unit and leaves the desired unit in its place.<\/p>\n<p id=\"import-auto-id1936373\"><strong>Solution for (a)<\/strong><\/p>\n<p id=\"import-auto-id2002968\">(1) Calculate average speed. Average speed is distance traveled divided by time of travel. (Take this definition as a given for now\u2014average speed and other motion concepts will be covered in a later module.) In equation form,<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-389\">[latex]\\text{average speed =}\\frac{\\text{distance}}{\\text{time}}\\text{.}[\/latex]<\/div>\n<p id=\"import-auto-id2546293\">(2) Substitute the given values for distance and time.<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-702\">[latex]\\text{average speed =}\\frac{\\text{10}\\text{.}0\\text{&nbsp;km}}{\\text{20}\\text{.}0\\text{&nbsp;min}}=0\\text{.}\\text{500}\\frac{\\text{&nbsp;km}}{\\text{&nbsp;min}}\\text{.}[\/latex]<\/div>\n<p id=\"import-auto-id1342839\">(3) Convert km\/min to km\/h: multiply by the conversion factor that will cancel minutes and leave hours. That conversion factor is [latex]\\text{60 min\/hr}[\/latex]. Thus,<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-583\">[latex]\\text{average speed =}0\\text{.}\\text{500}\\frac{\\text{&nbsp;km}}{\\text{&nbsp;min}}\u00d7\\frac{\\text{60}\\text{&nbsp;min}}{1\\text{&nbsp;h}}=\\text{30}\\text{.}0\\frac{\\text{&nbsp;km}}{\\text{&nbsp;h}}\\text{.}[\/latex]<\/div>\n<p id=\"import-auto-id2637111\"><strong>Discussion for (a)<\/strong><\/p>\n<p id=\"import-auto-id3084428\">To check your answer, consider the following:<\/p>\n<p id=\"import-auto-id1533540\">(1) Be sure that you have properly cancelled the units in the unit conversion. If you have written the unit conversion factor upside down, the units will not cancel properly in the equation. If you accidentally get the ratio upside down, then the units will not cancel; rather, they will give you the wrong units as follows:<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-593\">[latex]\\frac{\\text{&nbsp;km}}{\\text{min}}\u00d7\\frac{1\\text{&nbsp;hr}}{\\text{60}\\text{&nbsp;min}}=\\frac{1}{\\text{60}}\\frac{\\text{&nbsp;km}\\cdot \\text{hr}}{{\\text{&nbsp;min}}^{2}}\\text{,}[\/latex]<\/div>\n<p id=\"import-auto-id704163\">which are obviously not the desired units of km\/h.<\/p>\n<p id=\"import-auto-id2974712\">(2) Check that the units of the final answer are the desired units. The problem asked us to solve for average speed in units of km\/h and we have indeed obtained these units.<\/p>\n<p id=\"import-auto-id1552604\">(3) Check the significant figures. Because each of the values given in the problem has three significant figures, the answer should also have three significant figures. The answer 30.0 km\/hr does indeed have three significant figures, so this is appropriate. Note that the significant figures in the conversion factor are not relevant because an hour is <em data-effect=\"italics\">defined<\/em> to be 60 minutes, so the precision of the conversion factor is perfect.<\/p>\n<p id=\"import-auto-id3089353\">(4) Next, check whether the answer is reasonable. Let us consider some information from the problem\u2014if you travel 10 km in a third of an hour (20 min), you would travel three times that far in an hour. The answer does seem reasonable.<\/p>\n<p id=\"import-auto-id2609064\"><strong>Solution for (b)<\/strong><\/p>\n<p id=\"import-auto-id3164730\">There are several ways to convert the average speed into meters per second.<\/p>\n<p id=\"import-auto-id3136302\">(1) Start with the answer to (a) and convert km\/h to m\/s. Two conversion factors are needed\u2014one to convert hours to seconds, and another to convert kilometers to meters.<\/p>\n<p id=\"import-auto-id1324707\">(2) Multiplying by these yields<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-790\">[latex]\\text{Average speed}=\\text{30}\\text{.}0\\frac{\\text{km}}{\\text{h}}\u00d7\\frac{1\\phantom{\\rule{0.25em}{0ex}}\\text{h}}{\\text{3,600 s}}\u00d7\\frac{1,\\text{000}\\phantom{\\rule{0.25em}{0ex}}\\text{m}}{\\text{1 km}}\\text{,}[\/latex]<\/div>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-130\">[latex]\\text{Average speed}=8\\text{.}\\text{33}\\frac{\\text{m}}{\\text{s}}\\text{.}[\/latex]<\/div>\n<p id=\"import-auto-id1305929\"><strong>Discussion for (b)<\/strong><\/p>\n<p id=\"import-auto-id3204929\">If we had started with 0.500 km\/min, we would have needed different conversion factors, but the answer would have been the same: 8.33 m\/s.<\/p>\n<p id=\"import-auto-id2712034\">You may have noted that the answers in the worked example just covered were given to three digits. Why? When do you need to be concerned about the number of digits in something you calculate? Why not write down all the digits your calculator produces? The module <a href=\"\/contents\/4bba6a1c-a0e6-45c0-988c-0d5c23425670@7\">Accuracy, Precision, and Significant Figures<\/a> will help you answer these questions.<\/p>\n<\/div>\n<div data-type=\"note\" class=\"note\" data-has-label=\"true\" id=\"fs-id2706300\" data-label=\"\">\n<div data-type=\"title\" class=\"title\">Nonstandard Units<\/div>\n<p id=\"import-auto-id1599459\">While there are numerous types of units that we are all familiar with, there are others that are much more obscure. For example, a <strong>firkin<\/strong> is a unit of volume that was once used to measure beer. One firkin equals about 34 liters. To learn more about nonstandard units, use a dictionary or encyclopedia to research different \u201cweights and measures.\u201d Take note of any unusual units, such as a barleycorn, that are not listed in the text. Think about how the unit is defined and state its relationship to SI units.<\/p>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1956235\" data-print-placement=\"here\" data-element-type=\"check-understanding\" data-label=\"\">\n<div data-type=\"title\">Check Your Understanding<\/div>\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1959288\">\n<p id=\"import-auto-id1279620\">Some hummingbirds beat their wings more than 50 times per second. A scientist is measuring the time it takes for a hummingbird to beat its wings once. Which fundamental unit should the scientist use to describe the measurement? Which factor of 10 is the scientist likely to use to describe the motion precisely? Identify the metric prefix that corresponds to this factor of 10. <\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2683424\" data-print-placement=\"here\">\n<p id=\"import-auto-id3168169\">The scientist will measure the time between each movement using the fundamental unit of seconds. Because the wings beat so fast, the scientist will probably need to measure in milliseconds, or [latex]{\\text{10}}^{-3}[\/latex] seconds. (50 beats per second corresponds to 20 milliseconds per beat.)<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1780694\" data-print-placement=\"here\" data-element-type=\"check-understanding\" data-label=\"\">\n<div data-type=\"title\">Check Your Understanding<\/div>\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2785205\">\n<p id=\"import-auto-id2970927\">One cubic centimeter is equal to one milliliter. What does this tell you about the different units in the SI metric system?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2792998\" data-print-placement=\"here\">\n<p id=\"import-auto-id2607441\">The fundamental unit of length (meter) is probably used to create the derived unit of volume (liter). The measure of a milliliter is dependent on the measure of a centimeter.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"section-summary\" data-depth=\"1\" id=\"fs-id1448204\">\n<h1 data-type=\"title\">Summary<\/h1>\n<ul id=\"fs-id1415321\">\n<li id=\"import-auto-id1958750\">Physical quantities are a characteristic or property of an object that can be measured or calculated from other measurements.<\/li>\n<li>Units are standards for expressing and comparing the measurement of physical quantities. All units can be expressed as combinations of four fundamental units.<\/li>\n<li id=\"import-auto-id2946026\">The four fundamental units we will use in this text are the meter (for length), the kilogram (for mass), the second (for time), and the ampere (for electric current). These units are part of the metric system, which uses powers of 10 to relate quantities over the vast ranges encountered in nature.<\/li>\n<li id=\"import-auto-id1951848\">The four fundamental units are abbreviated as follows: meter, m; kilogram, kg; second, s; and ampere, A. The metric system also uses a standard set of prefixes to denote each order of magnitude greater than or lesser than the fundamental unit itself.<\/li>\n<li id=\"import-auto-id1439000\">Unit conversions involve changing a value expressed in one type of unit to another type of unit. This is done by using conversion factors, which are ratios relating equal quantities of different units.<\/li>\n<\/ul>\n<\/div>\n<div class=\"conceptual-questions\" data-depth=\"1\" id=\"fs-id3137968\" data-element-type=\"conceptual-questions\">\n<h1 data-type=\"title\">Conceptual Questions<\/h1>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3143663\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3143664\">\n<p id=\"import-auto-id2596654\">Identify some advantages of metric units.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"problems-exercises\" data-depth=\"1\" id=\"fs-id1569485\" data-element-type=\"problems-exercises\">\n<h1 data-type=\"title\">Problems &amp; Exercises<\/h1>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1434957\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1434958\">\n<p id=\"import-auto-id1290809\">The speed limit on some interstate highways is roughly 100 km\/h. (a) What is this in meters per second? (b) How many miles per hour is this?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2921458\">\n<ol id=\"import-auto-id1512938\" data-mark-prefix=\"(\" data-mark-suffix=\")\" data-number-style=\"lower-alpha\">\n<li>[latex]\\text{27}\\text{.}\\text{8 m\/s}[\/latex]<\/li>\n<li>[latex]\\text{62}\\text{.}\\text{1 mph}[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1544895\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1544896\">\n<p id=\"import-auto-id3146737\">A car is traveling at a speed of [latex]\\text{33 m\/s}[\/latex]. (a) What is its speed in kilometers per hour? (b) Is it exceeding the [latex]\\text{90 km\/h}[\/latex] speed limit?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1433050\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1433051\">\n<p id=\"import-auto-id3195918\">Show that [latex]1\\text{.}\\text{0 m\/s}=3\\text{.}\\text{6 km\/h}[\/latex]. Hint: Show the explicit steps involved in converting [latex]1\\text{.}\\text{0 m\/s}=3\\text{.}\\text{6 km\/h.}[\/latex]<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1441485\">\n<p id=\"import-auto-id1430228\">[latex]\\frac{\\text{1.0 m}}{s}=\\frac{1\\text{.}\\text{0 m}}{s}\u00d7\\frac{\\text{3600 s}}{\\text{1 hr}}\u00d7\\frac{1 km}{\\text{1000 m}}[\/latex]<\/p>\n<p id=\"import-auto-id2629093\">[latex]=3\\text{.}\\text{6 km\/h}[\/latex].<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1434985\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1434986\">\n<p id=\"import-auto-id3358370\">American football is played on a 100-yd-long field, excluding the end zones. How long is the field in meters? (Assume that 1 meter equals 3.281 feet.)<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1439792\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1439793\">\n<p id=\"import-auto-id1327449\">Soccer fields vary in size. A large soccer field is 115 m long and 85 m wide. What are its dimensions in feet and inches? (Assume that 1 meter equals 3.281 feet.)<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1484623\">\n<p id=\"import-auto-id2559751\">length: [latex]\\text{377 ft}[\/latex]; [latex]4\\text{.}\\text{53}\u00d7{\\text{10}}^{3}\\text{&nbsp;in}\\text{.}[\/latex] width: [latex]\\text{280&nbsp;ft}[\/latex]; [latex]3\\text{.}3\u00d7{\\text{10}}^{3}\\text{&nbsp;in}[\/latex].<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3159821\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3159822\">\n<p id=\"import-auto-id2723769\">What is the height in meters of a person who is 6 ft 1.0 in. tall? (Assume that 1 meter equals 39.37 in.)<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3159831\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3159832\">\n<p id=\"import-auto-id1569154\">Mount Everest, at 29,028 feet, is the tallest mountain on the Earth. What is its height in kilometers? (Assume that 1 kilometer equals 3,281 feet.)<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id3080571\">\n<p id=\"import-auto-id2601912\">[latex]8\\text{.}\\text{847 km}[\/latex]<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3158542\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3158543\">\n<p id=\"import-auto-id2912855\">The speed of sound is measured to be [latex]\\text{342 m\/s}[\/latex] on a certain day. What is this in km\/h?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3180898\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3180900\">\n<p id=\"import-auto-id3164687\">Tectonic plates are large segments of the Earth\u2019s crust that move slowly. Suppose that one such plate has an average speed of 4.0 cm\/year. (a) What distance does it move in 1 s at this speed? (b) What is its speed in kilometers per million years?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2637777\">\n<p id=\"import-auto-id1951052\">(a) [latex]1\\text{.}3\u00d7{\\text{10}}^{-9}\\text{&nbsp;m}[\/latex]<\/p>\n<p id=\"import-auto-id2632722\">(b) [latex]\\text{40 km\/My}[\/latex]<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1564148\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1564149\">\n<p id=\"import-auto-id3143596\">(a) Refer to <a href=\"#import-auto-id1677589\" class=\"autogenerated-content\">(Figure)<\/a> to determine the average distance between the Earth and the Sun. Then calculate the average speed of the Earth in its orbit in kilometers per second. (b) What is this in meters per second?<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"footnote-refs\">\n<h2 data-type=\"footnote-title\">Footnotes<\/h2>\n<ol>\n<li><a data-type=\"footnote-ref\" href=\"#footnote-ref1\">1<\/a> See <a href=\"\/contents\/aaf30a54-a356-4c5f-8c0d-2f55e4d20556@3\">Appendix A<\/a> for a discussion of powers of 10.<\/li>\n<\/ol>\n<\/div>\n<div data-type=\"glossary\" class=\"textbox shaded\">\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\n<dl class=\"definition\" id=\"import-auto-id3096670\">\n<dt>physical quantity <\/dt>\n<dd id=\"fs-id3105089\">a characteristic or property of an object that can be measured or calculated from other measurements<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id3136233\">\n<dt>units <\/dt>\n<dd id=\"fs-id3105099\"> a standard used for expressing and comparing measurements<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id2968885\">\n<dt>SI units <\/dt>\n<dd id=\"fs-id1577059\">the international system of units that scientists in most countries have agreed to use; includes units such as meters, liters, and grams<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id2582101\">\n<dt>English units<\/dt>\n<dd id=\"fs-id2018396\"> system of measurement used in the United States; includes units of measurement such as feet, gallons, and pounds<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id3401009\">\n<dt>fundamental units<\/dt>\n<dd id=\"fs-id2991354\"> units that can only be expressed relative to the procedure used to measure them<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id2512053\">\n<dt>derived units<\/dt>\n<dd id=\"fs-id3186991\"> units that can be calculated using algebraic combinations of the fundamental units<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id2771646\">\n<dt>second<\/dt>\n<dd id=\"fs-id3187001\"> the SI unit for time, abbreviated (s)<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id2910820\">\n<dt>meter<\/dt>\n<dd id=\"fs-id3201842\"> the SI unit for length, abbreviated (m)<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id2806926\">\n<dt>kilogram<\/dt>\n<dd id=\"fs-id2573988\"> the SI unit for mass, abbreviated (kg)<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id1990374\">\n<dt>metric system<\/dt>\n<dd id=\"fs-id2573998\"> a system in which values can be calculated in factors of 10<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id1950368\">\n<dt>order of magnitude<\/dt>\n<dd id=\"fs-id3348791\"> refers to the size of a quantity as it relates to a power of 10<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id2656746\">\n<dt>conversion factor<\/dt>\n<dd id=\"fs-id1434398\"> a ratio expressing how many of one unit are equal to another unit<\/dd>\n<\/dl>\n<\/div>\n\n","rendered":"<div class=\"textbox learning-objectives\">\n<h3 itemprop=\"educationalUse\">Learning Objectives<\/h3>\n<ul>\n<li>Perform unit conversions both in the SI and English units.\n<\/li>\n<li>Explain the most common prefixes in the SI units and be able to write them in scientific notation.<\/li>\n<\/ul>\n<\/div>\n<div class=\"bc-figure figure\" id=\"import-auto-id2657097\">\n<div class=\"bc-figcaption figcaption\">The distance from Earth to the Moon may seem immense, but it is just a tiny fraction of the distances from Earth to other celestial bodies. (credit: NASA)<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id3164906\" data-alt=\"A view of Earth from the Moon.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_01_02_01b.jpg\" data-media-type=\"image\/png\" alt=\"A view of Earth from the Moon.\" width=\"300\" \/><\/span><\/p>\n<\/div>\n<p id=\"import-auto-id2510075\">The range of objects and phenomena studied in physics is immense. From the incredibly short lifetime of a nucleus to the age of the Earth, from the tiny sizes of sub-nuclear particles to the vast distance to the edges of the known universe, from the force exerted by a jumping flea to the force between Earth and the Sun, there are enough factors of 10 to challenge the imagination of even the most experienced scientist. Giving numerical values for physical quantities and equations for physical principles allows us to understand nature much more deeply than does qualitative description alone. To comprehend these vast ranges, we must also have accepted units in which to express them. And we shall find that (even in the potentially mundane discussion of meters, kilograms, and seconds) a profound simplicity of nature appears\u2014all physical quantities can be expressed as combinations of only four fundamental physical quantities: length, mass, time, and electric current.<\/p>\n<p id=\"import-auto-id1675918\">We define a <span data-type=\"term\" id=\"import-auto-id1536256\">physical quantity<\/span> either by  <em data-effect=\"italics\">specifying how it is measured<\/em> or by <em data-effect=\"italics\"><em data-effect=\"italics\">stating how it is calculated<\/em><\/em> from other measurements. For example, we define distance and time by specifying methods for measuring them, whereas we define <em data-effect=\"italics\"><em data-effect=\"italics\">average speed<\/em><\/em> by stating that it is calculated as distance traveled divided by time of travel.<\/p>\n<p id=\"import-auto-id2985261\">Measurements of physical quantities are expressed in terms of <span data-type=\"term\" id=\"import-auto-id1666000\">units<\/span>, which are standardized values. For example, the length of a race, which is a physical quantity, can be expressed in units of meters (for sprinters) or kilometers (for distance runners). Without standardized units, it would be extremely difficult for scientists to express and compare measured values in a meaningful way. (See <a href=\"#import-auto-id2991258\" class=\"autogenerated-content\">(Figure)<\/a>.)<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id2991258\">\n<div class=\"bc-figcaption figcaption\">Distances given in unknown units are maddeningly useless.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id2750660\" data-alt=\"A boy looking at a map and trying to guess distances with unit of length mentioned as cables between two points.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_01_02_01a.jpg\" data-media-type=\"image\/jpg\" alt=\"A boy looking at a map and trying to guess distances with unit of length mentioned as cables between two points.\" height=\"225\" \/><\/span><\/p>\n<\/div>\n<p id=\"import-auto-id1284944\">There are two major systems of units used in the world: <span data-type=\"term\">SI units<\/span> (also known as the metric system) and <span data-type=\"term\">English units<\/span> (also known as the customary or imperial system). <strong>English units<\/strong> were historically used in nations once ruled by the British Empire and are still widely used in the United States. Virtually every other country in the world now uses SI units as the standard; the metric system is also the standard system agreed upon by scientists and mathematicians. The acronym \u201cSI\u201d is derived from the French <em data-effect=\"italics\">Syst\u00e8me International<\/em>.<\/p>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1964667\">\n<h1 data-type=\"title\">SI Units: Fundamental and Derived Units<\/h1>\n<p id=\"import-auto-id2605641\"><a href=\"#import-auto-id3094653\" class=\"autogenerated-content\">(Figure)<\/a> gives the fundamental SI units that are used throughout this textbook. This text uses non-SI units in a few applications where they are in very common use, such as the measurement of blood pressure in millimeters of mercury (mm Hg). Whenever non-SI units are discussed, they will be tied to SI units through conversions.<\/p>\n<table id=\"import-auto-id3094653\" summary=\"A table listing fundamental S I units with two rows. One row lists the physical quantities and the other lists their units.\">\n<caption><span data-type=\"title\">Fundamental SI Units<\/span><\/caption>\n<thead>\n<tr>\n<th><strong>Length<\/strong><\/th>\n<th><strong>Mass<\/strong><\/th>\n<th><strong>Time<\/strong><\/th>\n<th><strong>Electric Current<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>meter (m)<\/td>\n<td>kilogram (kg)<\/td>\n<td>second (s)<\/td>\n<td>ampere (A)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"import-auto-id2729047\">It is an intriguing fact that some physical quantities are more fundamental than others and that the most fundamental physical quantities can be defined <em data-effect=\"italics\"><em data-effect=\"italics\">only<\/em><\/em> in terms of the procedure used to measure them. The units in which they are measured are thus called <span data-type=\"term\" id=\"import-auto-id3097983\">fundamental units<\/span>. In this textbook, the fundamental physical quantities are taken to be length, mass, time, and electric current. (Note that electric current will not be introduced until much later in this text.) All other physical quantities, such as force and electric charge, can be expressed as algebraic combinations of length, mass, time, and current (for example, speed is length divided by time); these units are called <span data-type=\"term\">derived units<\/span>.<\/p>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id3102294\">\n<h1 data-type=\"title\">Units of Time, Length, and Mass: The Second, Meter, and Kilogram<\/h1>\n<div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id2929182\">\n<h2 data-type=\"title\">The Second<\/h2>\n<p id=\"import-auto-id1598785\">The SI unit for time, the <span data-type=\"term\" id=\"import-auto-id2526901\">second<\/span>(abbreviated s), has a long history. For many years it was defined as 1\/86,400 of a mean solar day. More recently, a new standard was adopted to gain greater accuracy and to define the second in terms of a non-varying, or constant, physical phenomenon (because the solar day is getting longer due to very gradual slowing of the Earth\u2019s rotation). Cesium atoms can be made to vibrate in a very steady way, and these vibrations can be readily observed and counted. In 1967 the second was redefined as the time required for 9,192,631,770 of these vibrations. (See <a href=\"#import-auto-id2575847\" class=\"autogenerated-content\">(Figure)<\/a>.) Accuracy in the fundamental units is essential, because all measurements are ultimately expressed in terms of fundamental units and can be no more accurate than are the fundamental units themselves.<\/p>\n<div class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">An atomic clock such as this one uses the vibrations of cesium atoms to keep time to a precision of better than a microsecond per year. The fundamental unit of time, the second, is based on such clocks. This image is looking down from the top of an atomic fountain nearly 30 feet tall! (credit: Steve Jurvetson\/Flickr)<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id1310868\" data-alt=\"A top view of an atomic fountain is shown. It measures time using the vibration of the cesium atom.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_01_02_02a.jpg\" data-media-type=\"image\/jpg\" alt=\"A top view of an atomic fountain is shown. It measures time using the vibration of the cesium atom.\" height=\"225\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id2998899\">\n<h2 data-type=\"title\">The Meter<\/h2>\n<p id=\"import-auto-id2837009\">The SI unit for length is the <span data-type=\"term\" id=\"import-auto-id1629056\">meter<\/span> (abbreviated m); its definition has also changed over time to become more accurate and precise. The meter was first defined in 1791 as 1\/10,000,000 of the distance from the equator to the North Pole. This measurement was improved in 1889 by redefining the meter to be the distance between two engraved lines on a platinum-iridium bar now kept near Paris. By 1960, it had become possible to define the meter even more accurately in terms of the wavelength of light, so it was again redefined as 1,650,763.73 wavelengths of orange light emitted by krypton atoms. In 1983, the meter was given its present definition (partly for greater accuracy) as the distance light travels in a vacuum in 1\/299,792,458 of a second. (See <a href=\"#import-auto-id1381492\" class=\"autogenerated-content\">(Figure)<\/a>.) This change defines the speed of light to be exactly 299,792,458 meters per second. The length of the meter will change if the speed of light is someday measured with greater accuracy.<\/p>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id2786029\">\n<h2 data-type=\"title\">The Kilogram<\/h2>\n<p id=\"import-auto-id3204634\">The SI unit for mass is the <span data-type=\"term\" id=\"import-auto-id1989656\">kilogram<\/span> (abbreviated kg); it is defined to be the mass of a platinum-iridium cylinder kept with the old meter standard at the International Bureau of Weights and Measures near Paris. Exact replicas of the standard kilogram are also kept at the United States\u2019 National Institute of Standards and Technology, or NIST, located in Gaithersburg, Maryland outside of Washington D.C., and at other locations around the world. The determination of all other masses can be ultimately traced to a comparison with the standard mass.<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id1381492\">\n<div class=\"bc-figcaption figcaption\">The meter is defined to be the distance light travels in 1\/299,792,458 of a second in a vacuum. Distance traveled is speed multiplied by time.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id2509382\" data-alt=\"Beam of light from a flashlight is represented by an arrow pointing right, traveling the length of a meter stick.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_01_02_03a.jpg\" data-media-type=\"image\/jpg\" alt=\"Beam of light from a flashlight is represented by an arrow pointing right, traveling the length of a meter stick.\" width=\"400\" \/><\/span><\/p>\n<\/div>\n<p id=\"import-auto-id1255984\">Electric current and its accompanying unit, the ampere, will be introduced in <a href=\"\/contents\/127f63f7-d67f-4710-8625-2b1d4128ef6b@2\">Introduction to Electric Current, Resistance, and Ohm&#8217;s Law<\/a> when electricity and magnetism are covered. The initial modules in this textbook are concerned with mechanics, fluids, heat, and waves. In these subjects all pertinent physical quantities can be expressed in terms of the fundamental units of length, mass, and time.<\/p>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id2559237\">\n<h1 data-type=\"title\">Metric Prefixes<\/h1>\n<p id=\"import-auto-id2789715\">SI units are part of the <span data-type=\"term\" id=\"import-auto-id2678122\">metric system<\/span>. The metric system is convenient for scientific and engineering calculations because the units are categorized by factors of 10. <a href=\"#import-auto-id2643474\" class=\"autogenerated-content\">(Figure)<\/a> gives metric prefixes and symbols used to denote various factors of 10.<\/p>\n<p id=\"import-auto-id1309728\">Metric systems have the advantage that conversions of units involve only powers of 10. There are 100 centimeters in a meter, 1000 meters in a kilometer, and so on. In nonmetric systems, such as the system of U.S. customary units, the relationships are not as simple\u2014there are 12 inches in a foot, 5280 feet in a mile, and so on. Another advantage of the metric system is that the same unit can be used over extremely large ranges of values simply by using an appropriate metric prefix. For example, distances in meters are suitable in construction, while distances in kilometers are appropriate for air travel, and the tiny measure of nanometers are convenient in optical design. With the metric system there is no need to invent new units for particular applications.<\/p>\n<p id=\"import-auto-id1577727\">The term <span data-type=\"term\" id=\"import-auto-id1363292\">order of magnitude<\/span> refers to the scale of a value expressed in the metric system. Each power of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-678cf27a50e5c98a241c4564cee34b2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> in the metric system represents a different order of magnitude. For example, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-e98c7113fd7bd1995f68dc4f5ebefe7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#49;&#125;&#44;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#50;&#125;&#44;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"99\" style=\"vertical-align: -4px;\" \/>, and so forth are all different orders of magnitude. All quantities that can be expressed as a product of a specific power of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-678cf27a50e5c98a241c4564cee34b2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> are said to be of the <em data-effect=\"italics\"><em data-effect=\"italics\">same<\/em><\/em> order of magnitude. For example, the number <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-caecea081a51566934705fc911aed8a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#56;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"27\" style=\"vertical-align: 0px;\" \/> can be written as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-abb2580ec747c4b33d1c2be97668428a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"34\" style=\"vertical-align: -1px;\" \/>, and the number <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4ef0e00c0fea5a89548c666a394eaa5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#52;&#53;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"27\" style=\"vertical-align: -1px;\" \/> can be written as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-942abe656c78e9963f1f790bfaaade9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#46;&#53;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#50;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"52\" style=\"vertical-align: -1px;\" \/> Thus, the numbers <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-caecea081a51566934705fc911aed8a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#56;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"27\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4ef0e00c0fea5a89548c666a394eaa5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#52;&#53;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"27\" style=\"vertical-align: -1px;\" \/> are of the same order of magnitude: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-54039560035b536fce86eaf4fcb9a831_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#50;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"28\" style=\"vertical-align: -1px;\" \/> Order of magnitude can be thought of as a ballpark estimate for the scale of a value. The diameter of an atom is on the order of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-a89f7d650aac478313b1cf5ce35fa03b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#57;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#109;&#44;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"60\" style=\"vertical-align: -3px;\" \/> while the diameter of the Sun is on the order of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-5a453577637ca147fb3326eaef613cad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#57;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#109;&#46;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"49\" style=\"vertical-align: -1px;\" \/><\/p>\n<div data-type=\"note\" class=\"note\" data-has-label=\"true\" id=\"fs-id2834817\" data-label=\"\">\n<div data-type=\"title\" class=\"title\">The Quest for Microscopic Standards for Basic Units<\/div>\n<p id=\"import-auto-id1113253\">The fundamental units described in this chapter are those that produce the greatest accuracy and precision in measurement. There is a sense among physicists that, because there is an underlying microscopic substructure to matter, it would be most satisfying to base our standards of measurement on microscopic objects and fundamental physical phenomena such as the speed of light. A microscopic standard has been accomplished for the standard of time, which is based on the oscillations of the cesium atom.<\/p>\n<p id=\"import-auto-id2596896\">The standard for length was once based on the wavelength of light (a small-scale length) emitted by a certain type of atom, but it has been supplanted by the more precise measurement of the speed of light. If it becomes possible to measure the mass of atoms or a particular arrangement of atoms such as a silicon sphere to greater precision than the kilogram standard, it may become possible to base mass measurements on the small scale. There are also possibilities that electrical phenomena on the small scale may someday allow us to base a unit of charge on the charge of electrons and protons, but at present current and charge are related to large-scale currents and forces between wires.<\/p>\n<\/div>\n<table id=\"import-auto-id2643474\" summary=\"A table listing metric prefixes for powers of ten and their symbols. The table has the four columns prefix, value, symbol, and example and each row mentions one example.\">\n<caption><span data-type=\"title\">Metric Prefixes for Powers of 10 and their Symbols<\/span><\/caption>\n<thead>\n<tr>\n<th>Prefix<\/th>\n<th>Symbol<\/th>\n<th>Value<a data-type=\"footnote-number\" href=\"#footnote1\"><sup>1<\/sup><\/a><\/th>\n<th colspan=\"4\">Example (some are approximate)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>exa<\/td>\n<td>E<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-8dbabd23a7fac22845843b03f7e895be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#56;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>exameter<\/td>\n<td>Em<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-ef20b67715f34d7710303b8743179fdb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#56;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"52\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>distance light travels in a century<\/td>\n<\/tr>\n<tr>\n<td>peta<\/td>\n<td>P<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-e3f95db434a3c915e4c9a8a87790a325_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>petasecond<\/td>\n<td>Ps<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-e5e7823601e3f0bdcb9faf251b03a98e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#53;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#115;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"44\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>30 million years<\/td>\n<\/tr>\n<tr>\n<td>tera<\/td>\n<td>T<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-d3434d6986d40e658dbed05d956463c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>terawatt<\/td>\n<td>TW<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4963e20fe55778cfba50db70f2b88d3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#50;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#87;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>powerful laser output<\/td>\n<\/tr>\n<tr>\n<td>giga<\/td>\n<td>G<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-6a99d177c4532b773c8d3dfefa143aa8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"24\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>gigahertz<\/td>\n<td>GHz<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-da217d6a5f431ea3a31bcbedce4f13ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#57;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#72;&#122;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"51\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>a microwave frequency<\/td>\n<\/tr>\n<tr>\n<td>mega<\/td>\n<td>M<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-bb4f3b6229e4491678fa3397b38ae5cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"24\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>megacurie<\/td>\n<td>MCi<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-3cfbb9f388757b869b5c766e9ac514db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#54;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#67;&#105;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"48\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>high radioactivity<\/td>\n<\/tr>\n<tr>\n<td>kilo<\/td>\n<td>k<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-2785a351d5c590d8be7d440e0bed118e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"24\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>kilometer<\/td>\n<td>km<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-ca4e09d32b5053854d9eb98433cc61bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#51;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"45\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>about 6\/10 mile<\/td>\n<\/tr>\n<tr>\n<td>hecto<\/td>\n<td>h<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-e7bd98de0384b10ed8ae97aedde29cf6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"24\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>hectoliter<\/td>\n<td>hL<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-fe1cb1ff1fcc397d7f8cb6c3b9da4a39_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#50;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#76;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>26 gallons<\/td>\n<\/tr>\n<tr>\n<td>deka<\/td>\n<td>da<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-79ca75ad4f343210334e61c3803fe309_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"23\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>dekagram<\/td>\n<td>dag<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-77963133ef1f5937bc7a694cff4f234a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#49;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#103;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -3px;\" \/><\/td>\n<td>teaspoon of butter<\/td>\n<\/tr>\n<tr>\n<td>\u2014<\/td>\n<td>\u2014<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-1a61edf4aeb88640cbeb503dd81c9216_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"24\" style=\"vertical-align: -1px;\" \/> (=1)<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>deci<\/td>\n<td>d<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-21de8d1ebee1ed42faec8070ac281b9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"34\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>deciliter<\/td>\n<td>dL<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-29a04675acf2ac4b652f3812457ed952_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#49;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#76;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"52\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>less than half a soda<\/td>\n<\/tr>\n<tr>\n<td>centi<\/td>\n<td>c<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-00277247aadf96758bd6a1f05a0b4797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"35\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>centimeter<\/td>\n<td>cm<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-5c1808e7b453694b34b41aca0915ecb8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#50;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>fingertip thickness<\/td>\n<\/tr>\n<tr>\n<td>milli<\/td>\n<td>m<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-0d7df9bde8396796fb513dfd4dcc68bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"35\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>millimeter<\/td>\n<td>mm<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-e6e8219e5d215aa5a2c7ed55a337b192_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#51;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>flea at its shoulders<\/td>\n<\/tr>\n<tr>\n<td>micro<\/td>\n<td>\u00b5<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-c5c15597ff82445df5bbb3bf26caff01_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"35\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>micrometer<\/td>\n<td>\u00b5m<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-d76c28b400a994fb23e389633aad64e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#54;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>detail in microscope<\/td>\n<\/tr>\n<tr>\n<td>nano<\/td>\n<td>n<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-624033533a4ebd9c5febf5c041e1b01e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"35\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>nanogram<\/td>\n<td>ng<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-32dfc9f7354950e6cd7a830b20a07ff1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#57;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#103;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"50\" style=\"vertical-align: -3px;\" \/><\/td>\n<td>small speck of dust<\/td>\n<\/tr>\n<tr>\n<td>pico<\/td>\n<td>p<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-d9eae96c862e125541ca72fa5770eece_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>picofarad<\/td>\n<td>pF<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-c88f8ccbdae2ebee295c356bf38f0442_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#50;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#70;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"59\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>small capacitor in radio<\/td>\n<\/tr>\n<tr>\n<td>femto<\/td>\n<td>f<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-ef004d163fc948bb0b584918746d6253_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>femtometer<\/td>\n<td>fm<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-3319d2fbc227330800abace7d1959b7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#53;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"63\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>size of a proton<\/td>\n<\/tr>\n<tr>\n<td>atto<\/td>\n<td>a<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4abafb5918efc43b2e827a3edd11e734_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#56;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>attosecond<\/td>\n<td>as<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-fada3a4e7ce8f28d79767bc9258fd02e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#56;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#115;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>time light crosses an atom<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1936382\">\n<h1 data-type=\"title\">Known Ranges of Length, Mass, and Time<\/h1>\n<p id=\"import-auto-id2688624\">The vastness of the universe and the breadth over which physics applies are illustrated by the wide range of examples of known lengths, masses, and times in <a href=\"#import-auto-id1677589\" class=\"autogenerated-content\">(Figure)<\/a>. Examination of this table will give you some feeling for the range of possible topics and numerical values. (See <a href=\"#import-auto-id3143533\" class=\"autogenerated-content\">(Figure)<\/a> and <a href=\"#import-auto-id3083060\" class=\"autogenerated-content\">(Figure)<\/a>.)<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id3143533\">\n<div class=\"bc-figcaption figcaption\">Tiny phytoplankton swims among crystals of ice in the Antarctic Sea. They range from a few micrometers to as much as 2 millimeters in length. (credit: Prof. Gordon T. Taylor, Stony Brook University; NOAA Corps Collections)<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id3440141\" data-alt=\"A magnified image of tiny phytoplankton swimming among the crystal of ice.[\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_01_02_04a.jpg\" data-media-type=\"image\/jpg\" alt=\"A magnified image of tiny phytoplankton swimming among the crystal of ice.[\" width=\"250\" \/><\/span><\/p>\n<\/div>\n<div class=\"bc-figure figure\" id=\"import-auto-id3083060\">\n<div class=\"bc-figcaption figcaption\">Galaxies collide 2.4 billion light years away from Earth. The tremendous range of observable phenomena in nature challenges the imagination. (credit: NASA\/CXC\/UVic.\/A. Mahdavi et al. Optical\/lensing: CFHT\/UVic.\/H. Hoekstra et al.)<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id2822519\" data-alt=\"A view of Abell Galaxy with some bright stars and some hot gases.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_01_02_05a.jpg\" data-media-type=\"image\/jpg\" alt=\"A view of Abell Galaxy with some bright stars and some hot gases.\" height=\"250\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1305702\">\n<h1 data-type=\"title\">Unit Conversion and Dimensional Analysis<\/h1>\n<p id=\"import-auto-id1959437\">It is often necessary to convert from one type of unit to another. For example, if you are reading a European cookbook, some quantities may be expressed in units of liters and you need to convert them to cups. Or, perhaps you are reading walking directions from one location to another and you are interested in how many miles you will be walking. In this case, you will need to convert units of feet to miles.<\/p>\n<p id=\"import-auto-id1430021\">Let us consider a simple example of how to convert units. Let us say that we want to convert 80 meters (m) to kilometers (km).<\/p>\n<p id=\"import-auto-id1595008\">The first thing to do is to list the units that you have and the units that you want to convert to. In this case, we have units in <em data-effect=\"italics\"><em data-effect=\"italics\">meters<\/em><\/em> and we want to convert to <em data-effect=\"italics\"><em data-effect=\"italics\">kilometers<\/em><\/em>.<\/p>\n<p id=\"import-auto-id3083046\">Next, we need to determine a <span data-type=\"term\" id=\"import-auto-id2657858\">conversion factor<\/span> relating meters to kilometers. A conversion factor is a ratio expressing how many of one unit are equal to another unit. For example, there are 12 inches in 1 foot, 100 centimeters in 1 meter, 60 seconds in 1 minute, and so on. In this case, we know that there are 1,000 meters in 1 kilometer.<\/p>\n<p id=\"import-auto-id2675967\">Now we can set up our unit conversion. We will write the units that we have and then multiply them by the conversion factor so that the units cancel out, as shown:<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-442\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-680c744ee286c02476388aed038ba130_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#48;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#125;&#125;&times;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#32;&#107;&#109;&#125;&#125;&#123;&#49;&#48;&#48;&#48;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#125;&#125;&#125;&#61;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#48;&#56;&#48;&#32;&#107;&#109;&#46;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"186\" style=\"vertical-align: -12px;\" \/><\/div>\n<p id=\"import-auto-id3150430\">Note that the unwanted m unit cancels, leaving only the desired km unit. You can use this method to convert between any types of unit.<\/p>\n<p id=\"import-auto-id2635975\">Click <a href=\"\/contents\/72343285-683e-46d9-a6c2-5de097e36ff9@5\" class=\"autogenerated-content\">(Figure)<\/a> for a more complete list of conversion factors.<\/p>\n<table id=\"import-auto-id1677589\" summary=\"A table is listing approximate values of length, mass, and time with each row containing an example of these.\">\n<caption><span data-type=\"title\">Approximate Values of Length, Mass, and Time<\/span><\/caption>\n<thead>\n<tr>\n<th colspan=\"2\">Lengths in meters<\/th>\n<th colspan=\"2\">Masses in kilograms (more precise values in parentheses)<\/th>\n<th colspan=\"2\">Times in seconds (more precise values in parentheses)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4abafb5918efc43b2e827a3edd11e734_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#56;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Present experimental limit to smallest observable detail<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-fa88271462af798011d8ba8307d27f30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#48;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Mass of an electron <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-841d84fbaf3e7ddd67d56b7989e15058_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#49;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#49;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#107;&#103;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"115\" style=\"vertical-align: -7px;\" \/><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-373fac0d0467162a216877063969ff90_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Time for light to cross a proton<\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-ef004d163fc948bb0b584918746d6253_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Diameter of a proton<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-f58d2bccd2a3a0ed0d8d98ce02e8f595_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#55;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Mass of a hydrogen atom <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-1c39ee05958953e0375209269fd6500b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#55;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#55;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#107;&#103;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"115\" style=\"vertical-align: -7px;\" \/> <\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-58c892034e255e63bd755b20006125cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Mean life of an extremely unstable nucleus<\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-c903d3020122e97084703d427a723b81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Diameter of a uranium nucleus<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-ef004d163fc948bb0b584918746d6253_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Mass of a bacterium<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-ef004d163fc948bb0b584918746d6253_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Time for one oscillation of visible light<\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-6561168cb38decaf88b9304e80bc499e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Diameter of a hydrogen atom<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-fef6fd358ce5d6e82e9f07fc653dc286_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"35\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Mass of a mosquito<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-6920fae76647ef63b4989fef1071252c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Time for one vibration of an atom in a solid<\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4efedf45694be4966a911200ccbf6369_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"35\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Thickness of membranes in cells of living organisms<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-00277247aadf96758bd6a1f05a0b4797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"35\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Mass of a hummingbird<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4efedf45694be4966a911200ccbf6369_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"35\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Time for one oscillation of an FM radio wave<\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-c5c15597ff82445df5bbb3bf26caff01_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"35\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Wavelength of visible light<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-83fc2e1bddffa7fe02203355d535c81a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Mass of a liter of water (about a quart)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-0d7df9bde8396796fb513dfd4dcc68bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"35\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Duration of a nerve impulse<\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-0d7df9bde8396796fb513dfd4dcc68bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"35\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Size of a grain of sand<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-e7bd98de0384b10ed8ae97aedde29cf6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"24\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Mass of a person<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-83fc2e1bddffa7fe02203355d535c81a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Time for one heartbeat<\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-83fc2e1bddffa7fe02203355d535c81a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Height of a 4-year-old child<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-2785a351d5c590d8be7d440e0bed118e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"24\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Mass of a car<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-986c62baa9c284af4cb88d7231e25b07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"24\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>One day <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-659e930f549d4571cc2048ebf4ffef4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#52;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#52;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"80\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-e7bd98de0384b10ed8ae97aedde29cf6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"24\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Length of a football field<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-df06742a0814878d770e1581a4873884_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"24\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Mass of a large ship <\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-260e04d6350724b3c44f1f36b65aced3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"24\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>One year (y) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-61702d06e101d4bfb8c7614baf44c28f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#54;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#55;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"80\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-7b68db8e1bb6f8709deb70607bebe181_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"24\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Greatest ocean depth<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-d3434d6986d40e658dbed05d956463c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Mass of a large iceberg<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-6a99d177c4532b773c8d3dfefa143aa8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"24\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>About half the life expectancy of a human<\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-260e04d6350724b3c44f1f36b65aced3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"24\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Diameter of the Earth<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-e3f95db434a3c915e4c9a8a87790a325_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Mass of the nucleus of a comet<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4ec0321b816fba7fd7f3e5205ca148ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"30\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Recorded history<\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4ec0321b816fba7fd7f3e5205ca148ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"30\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Distance from the Earth to the Sun<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-a9a4036ea4325d4bc841aaf2dbfa8a60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Mass of the Moon <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-e561748fa61dddb5a5dc1ba87d7fa237_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#53;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#50;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#107;&#103;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"105\" style=\"vertical-align: -7px;\" \/><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-f195473e9476ba688bacb289d4f8d00c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#55;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Age of the Earth<\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-2eaba30ca0d6c0607e54cb9cfb55d5b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Distance traveled by light in 1 year (a light year)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-51462ad6ef250209af3cd3b21ee0b864_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Mass of the Earth <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-d29534ba7c6574a6c8ea507b7a9785e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#57;&#55;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#52;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#107;&#103;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"105\" style=\"vertical-align: -7px;\" \/><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-8dbabd23a7fac22845843b03f7e895be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#56;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Age of the universe<\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-14f8213433a1a119e524097950706871_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"30\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Diameter of the Milky Way galaxy<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-d0e15b8c6e3ee1720c89593e1086b406_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#48;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Mass of the Sun <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-34c7eb078c959b63311ec8e9fe15eec5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#57;&#57;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#48;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#107;&#103;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"105\" style=\"vertical-align: -7px;\" \/><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-772ebe33b7ba72663da1b3e3d17ff4f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Distance from the Earth to the nearest large galaxy (Andromeda)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-b579c2fda7ec64f699a018416b4f7855_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#52;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Mass of the Milky Way galaxy (current upper limit)<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-7edeab1e4dfdd3eddafd98078f407dc5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Distance from the Earth to the edges of the known universe<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-123ca0e6c6579dbc53f7dff3e0518386_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#53;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>Mass of the known universe (current upper limit)<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div data-type=\"example\" class=\"textbox examples\" id=\"fs-id2747928\">\n<div data-type=\"title\" class=\"title\">Unit Conversions: A Short Drive Home<\/div>\n<p id=\"import-auto-id3204574\">Suppose that you drive the 10.0 km from your university to home in 20.0 min. Calculate your average speed (a) in kilometers per hour (km\/h) and (b) in meters per second (m\/s). (Note: Average speed is distance traveled divided by time of travel.)<\/p>\n<p id=\"import-auto-id2636340\"><strong>Strategy<\/strong><\/p>\n<p id=\"import-auto-id1951954\">First we calculate the average speed using the given units. Then we can get the average speed into the desired units by picking the correct conversion factor and multiplying by it. The correct conversion factor is the one that cancels the unwanted unit and leaves the desired unit in its place.<\/p>\n<p id=\"import-auto-id1936373\"><strong>Solution for (a)<\/strong><\/p>\n<p id=\"import-auto-id2002968\">(1) Calculate average speed. Average speed is distance traveled divided by time of travel. (Take this definition as a given for now\u2014average speed and other motion concepts will be covered in a later module.) In equation form,<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-389\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-ef2d5a464a62a6b281a11a520db4bde0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#118;&#101;&#114;&#97;&#103;&#101;&#32;&#115;&#112;&#101;&#101;&#100;&#32;&#61;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#100;&#105;&#115;&#116;&#97;&#110;&#99;&#101;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#105;&#109;&#101;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"183\" style=\"vertical-align: -7px;\" \/><\/div>\n<p id=\"import-auto-id2546293\">(2) Substitute the given values for distance and time.<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-702\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-bcc4c24b09cefa3798187089276d8e13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#118;&#101;&#114;&#97;&#103;&#101;&#32;&#115;&#112;&#101;&#101;&#100;&#32;&#61;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#107;&#109;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#109;&#105;&#110;&#125;&#125;&#61;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#53;&#48;&#48;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#107;&#109;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#109;&#105;&#110;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"282\" style=\"vertical-align: -7px;\" \/><\/div>\n<p id=\"import-auto-id1342839\">(3) Convert km\/min to km\/h: multiply by the conversion factor that will cancel minutes and leave hours. That conversion factor is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-09b38afef92e1fdc62e70d90c4e364cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#48;&#32;&#109;&#105;&#110;&#47;&#104;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"80\" style=\"vertical-align: -4px;\" \/>. Thus,<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-583\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-36d15d61a87d2a0551412869f9240027_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#118;&#101;&#114;&#97;&#103;&#101;&#32;&#115;&#112;&#101;&#101;&#100;&#32;&#61;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#53;&#48;&#48;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#107;&#109;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#109;&#105;&#110;&#125;&#125;&times;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#109;&#105;&#110;&#125;&#125;&#123;&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#104;&#125;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#107;&#109;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#104;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"330\" style=\"vertical-align: -7px;\" \/><\/div>\n<p id=\"import-auto-id2637111\"><strong>Discussion for (a)<\/strong><\/p>\n<p id=\"import-auto-id3084428\">To check your answer, consider the following:<\/p>\n<p id=\"import-auto-id1533540\">(1) Be sure that you have properly cancelled the units in the unit conversion. If you have written the unit conversion factor upside down, the units will not cancel properly in the equation. If you accidentally get the ratio upside down, then the units will not cancel; rather, they will give you the wrong units as follows:<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-593\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-85bff527a82ccff1d0a62fde50b4408f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#107;&#109;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#105;&#110;&#125;&#125;&times;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#104;&#114;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#109;&#105;&#110;&#125;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#48;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#107;&#109;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#104;&#114;&#125;&#125;&#123;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#109;&#105;&#110;&#125;&#125;&#94;&#123;&#50;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#44;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"160\" style=\"vertical-align: -9px;\" \/><\/div>\n<p id=\"import-auto-id704163\">which are obviously not the desired units of km\/h.<\/p>\n<p id=\"import-auto-id2974712\">(2) Check that the units of the final answer are the desired units. The problem asked us to solve for average speed in units of km\/h and we have indeed obtained these units.<\/p>\n<p id=\"import-auto-id1552604\">(3) Check the significant figures. Because each of the values given in the problem has three significant figures, the answer should also have three significant figures. The answer 30.0 km\/hr does indeed have three significant figures, so this is appropriate. Note that the significant figures in the conversion factor are not relevant because an hour is <em data-effect=\"italics\">defined<\/em> to be 60 minutes, so the precision of the conversion factor is perfect.<\/p>\n<p id=\"import-auto-id3089353\">(4) Next, check whether the answer is reasonable. Let us consider some information from the problem\u2014if you travel 10 km in a third of an hour (20 min), you would travel three times that far in an hour. The answer does seem reasonable.<\/p>\n<p id=\"import-auto-id2609064\"><strong>Solution for (b)<\/strong><\/p>\n<p id=\"import-auto-id3164730\">There are several ways to convert the average speed into meters per second.<\/p>\n<p id=\"import-auto-id3136302\">(1) Start with the answer to (a) and convert km\/h to m\/s. Two conversion factors are needed\u2014one to convert hours to seconds, and another to convert kilometers to meters.<\/p>\n<p id=\"import-auto-id1324707\">(2) Multiplying by these yields<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-790\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-e444774f7cd848170816d581edce8cd9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#65;&#118;&#101;&#114;&#97;&#103;&#101;&#32;&#115;&#112;&#101;&#101;&#100;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#107;&#109;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#104;&#125;&#125;&times;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#104;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#44;&#54;&#48;&#48;&#32;&#115;&#125;&#125;&times;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#48;&#48;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#32;&#107;&#109;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#44;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"290\" style=\"vertical-align: -9px;\" \/><\/div>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-130\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-609a2fe1d05bcbcb75b7320fc31f8990_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#65;&#118;&#101;&#114;&#97;&#103;&#101;&#32;&#115;&#112;&#101;&#101;&#100;&#125;&#61;&#56;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#51;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"186\" style=\"vertical-align: -6px;\" \/><\/div>\n<p id=\"import-auto-id1305929\"><strong>Discussion for (b)<\/strong><\/p>\n<p id=\"import-auto-id3204929\">If we had started with 0.500 km\/min, we would have needed different conversion factors, but the answer would have been the same: 8.33 m\/s.<\/p>\n<p id=\"import-auto-id2712034\">You may have noted that the answers in the worked example just covered were given to three digits. Why? When do you need to be concerned about the number of digits in something you calculate? Why not write down all the digits your calculator produces? The module <a href=\"\/contents\/4bba6a1c-a0e6-45c0-988c-0d5c23425670@7\">Accuracy, Precision, and Significant Figures<\/a> will help you answer these questions.<\/p>\n<\/div>\n<div data-type=\"note\" class=\"note\" data-has-label=\"true\" id=\"fs-id2706300\" data-label=\"\">\n<div data-type=\"title\" class=\"title\">Nonstandard Units<\/div>\n<p id=\"import-auto-id1599459\">While there are numerous types of units that we are all familiar with, there are others that are much more obscure. For example, a <strong>firkin<\/strong> is a unit of volume that was once used to measure beer. One firkin equals about 34 liters. To learn more about nonstandard units, use a dictionary or encyclopedia to research different \u201cweights and measures.\u201d Take note of any unusual units, such as a barleycorn, that are not listed in the text. Think about how the unit is defined and state its relationship to SI units.<\/p>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1956235\" data-print-placement=\"here\" data-element-type=\"check-understanding\" data-label=\"\">\n<div data-type=\"title\">Check Your Understanding<\/div>\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1959288\">\n<p id=\"import-auto-id1279620\">Some hummingbirds beat their wings more than 50 times per second. A scientist is measuring the time it takes for a hummingbird to beat its wings once. Which fundamental unit should the scientist use to describe the measurement? Which factor of 10 is the scientist likely to use to describe the motion precisely? Identify the metric prefix that corresponds to this factor of 10. <\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2683424\" data-print-placement=\"here\">\n<p id=\"import-auto-id3168169\">The scientist will measure the time between each movement using the fundamental unit of seconds. Because the wings beat so fast, the scientist will probably need to measure in milliseconds, or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-0d7df9bde8396796fb513dfd4dcc68bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"35\" style=\"vertical-align: -1px;\" \/> seconds. (50 beats per second corresponds to 20 milliseconds per beat.)<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1780694\" data-print-placement=\"here\" data-element-type=\"check-understanding\" data-label=\"\">\n<div data-type=\"title\">Check Your Understanding<\/div>\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2785205\">\n<p id=\"import-auto-id2970927\">One cubic centimeter is equal to one milliliter. What does this tell you about the different units in the SI metric system?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2792998\" data-print-placement=\"here\">\n<p id=\"import-auto-id2607441\">The fundamental unit of length (meter) is probably used to create the derived unit of volume (liter). The measure of a milliliter is dependent on the measure of a centimeter.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"section-summary\" data-depth=\"1\" id=\"fs-id1448204\">\n<h1 data-type=\"title\">Summary<\/h1>\n<ul id=\"fs-id1415321\">\n<li id=\"import-auto-id1958750\">Physical quantities are a characteristic or property of an object that can be measured or calculated from other measurements.<\/li>\n<li>Units are standards for expressing and comparing the measurement of physical quantities. All units can be expressed as combinations of four fundamental units.<\/li>\n<li id=\"import-auto-id2946026\">The four fundamental units we will use in this text are the meter (for length), the kilogram (for mass), the second (for time), and the ampere (for electric current). These units are part of the metric system, which uses powers of 10 to relate quantities over the vast ranges encountered in nature.<\/li>\n<li id=\"import-auto-id1951848\">The four fundamental units are abbreviated as follows: meter, m; kilogram, kg; second, s; and ampere, A. The metric system also uses a standard set of prefixes to denote each order of magnitude greater than or lesser than the fundamental unit itself.<\/li>\n<li id=\"import-auto-id1439000\">Unit conversions involve changing a value expressed in one type of unit to another type of unit. This is done by using conversion factors, which are ratios relating equal quantities of different units.<\/li>\n<\/ul>\n<\/div>\n<div class=\"conceptual-questions\" data-depth=\"1\" id=\"fs-id3137968\" data-element-type=\"conceptual-questions\">\n<h1 data-type=\"title\">Conceptual Questions<\/h1>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3143663\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3143664\">\n<p id=\"import-auto-id2596654\">Identify some advantages of metric units.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"problems-exercises\" data-depth=\"1\" id=\"fs-id1569485\" data-element-type=\"problems-exercises\">\n<h1 data-type=\"title\">Problems &amp; Exercises<\/h1>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1434957\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1434958\">\n<p id=\"import-auto-id1290809\">The speed limit on some interstate highways is roughly 100 km\/h. (a) What is this in meters per second? (b) How many miles per hour is this?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2921458\">\n<ol id=\"import-auto-id1512938\" data-mark-prefix=\"(\" data-mark-suffix=\")\" data-number-style=\"lower-alpha\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-6806a421d6ff556a628571813c54a255_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#55;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#56;&#32;&#109;&#47;&#115;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"68\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-85d136231228898c1ab9feda984f8d19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#50;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#32;&#109;&#112;&#104;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"72\" style=\"vertical-align: -3px;\" \/><\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1544895\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1544896\">\n<p id=\"import-auto-id3146737\">A car is traveling at a speed of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-fcb9b210ac743eaf3e4f701857fd2117_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#51;&#32;&#109;&#47;&#115;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"55\" style=\"vertical-align: -4px;\" \/>. (a) What is its speed in kilometers per hour? (b) Is it exceeding the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-7dffc7cca7eae6d1f71f6e883f338216_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#57;&#48;&#32;&#107;&#109;&#47;&#104;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"67\" style=\"vertical-align: -4px;\" \/> speed limit?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1433050\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1433051\">\n<p id=\"import-auto-id3195918\">Show that <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-feddb7fcc792df4bac5dbbe2124db270_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#32;&#109;&#47;&#115;&#125;&#61;&#51;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#32;&#107;&#109;&#47;&#104;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"153\" style=\"vertical-align: -4px;\" \/>. Hint: Show the explicit steps involved in converting <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-d99f4368e25c22bd7d477be9c94d662b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#32;&#109;&#47;&#115;&#125;&#61;&#51;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#32;&#107;&#109;&#47;&#104;&#46;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"157\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1441485\">\n<p id=\"import-auto-id1430228\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-c7c393914601bff02347b05713eff00a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#46;&#48;&#32;&#109;&#125;&#125;&#123;&#115;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#32;&#109;&#125;&#125;&#123;&#115;&#125;&times;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#54;&#48;&#48;&#32;&#115;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#32;&#104;&#114;&#125;&#125;&times;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#32;&#107;&#109;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#48;&#48;&#32;&#109;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"184\" style=\"vertical-align: -7px;\" \/><\/p>\n<p id=\"import-auto-id2629093\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-48678953c86753325ac0fdec2cfb93aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#61;&#51;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#32;&#107;&#109;&#47;&#104;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"90\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1434985\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1434986\">\n<p id=\"import-auto-id3358370\">American football is played on a 100-yd-long field, excluding the end zones. How long is the field in meters? (Assume that 1 meter equals 3.281 feet.)<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1439792\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1439793\">\n<p id=\"import-auto-id1327449\">Soccer fields vary in size. A large soccer field is 115 m long and 85 m wide. What are its dimensions in feet and inches? (Assume that 1 meter equals 3.281 feet.)<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1484623\">\n<p id=\"import-auto-id2559751\">length: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-de48a0b1b672dd9703c4ab8f4f236c60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#55;&#55;&#32;&#102;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"44\" style=\"vertical-align: -1px;\" \/>; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-ce6d24c8998a40232034fbd03fb7e772_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#53;&#51;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#51;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#105;&#110;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -1px;\" \/> width: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-2b974d17a7c4aa43f392e56f062ec13b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#56;&#48;&#32;&#102;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"44\" style=\"vertical-align: -1px;\" \/>; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-371ed2398ed3136ee39341a33026a2ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#51;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#51;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#105;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"69\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3159821\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3159822\">\n<p id=\"import-auto-id2723769\">What is the height in meters of a person who is 6 ft 1.0 in. tall? (Assume that 1 meter equals 39.37 in.)<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3159831\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3159832\">\n<p id=\"import-auto-id1569154\">Mount Everest, at 29,028 feet, is the tallest mountain on the Earth. What is its height in kilometers? (Assume that 1 kilometer equals 3,281 feet.)<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id3080571\">\n<p id=\"import-auto-id2601912\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-cea72d310eec86121e43c9a8a9864302_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#56;&#52;&#55;&#32;&#107;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"70\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3158542\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3158543\">\n<p id=\"import-auto-id2912855\">The speed of sound is measured to be <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-596745c2ee9d7fffa3534b6bd5be24f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#52;&#50;&#32;&#109;&#47;&#115;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"64\" style=\"vertical-align: -4px;\" \/> on a certain day. What is this in km\/h?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3180898\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3180900\">\n<p id=\"import-auto-id3164687\">Tectonic plates are large segments of the Earth\u2019s crust that move slowly. Suppose that one such plate has an average speed of 4.0 cm\/year. (a) What distance does it move in 1 s at this speed? (b) What is its speed in kilometers per million years?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2637777\">\n<p id=\"import-auto-id1951052\">(a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-2bcb3ccb555bb29e35d5f7a27e6f269e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#51;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#57;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"79\" style=\"vertical-align: -1px;\" \/><\/p>\n<p id=\"import-auto-id2632722\">(b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-e7914ce6ba5f6dfae3fdf4691d22f6b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#52;&#48;&#32;&#107;&#109;&#47;&#77;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1564148\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1564149\">\n<p id=\"import-auto-id3143596\">(a) Refer to <a href=\"#import-auto-id1677589\" class=\"autogenerated-content\">(Figure)<\/a> to determine the average distance between the Earth and the Sun. Then calculate the average speed of the Earth in its orbit in kilometers per second. (b) What is this in meters per second?<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"footnote-refs\">\n<h2 data-type=\"footnote-title\">Footnotes<\/h2>\n<ol>\n<li><a data-type=\"footnote-ref\" href=\"#footnote-ref1\">1<\/a> See <a href=\"\/contents\/aaf30a54-a356-4c5f-8c0d-2f55e4d20556@3\">Appendix A<\/a> for a discussion of powers of 10.<\/li>\n<\/ol>\n<\/div>\n<div data-type=\"glossary\" class=\"textbox shaded\">\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\n<dl class=\"definition\" id=\"import-auto-id3096670\">\n<dt>physical quantity <\/dt>\n<dd id=\"fs-id3105089\">a characteristic or property of an object that can be measured or calculated from other measurements<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id3136233\">\n<dt>units <\/dt>\n<dd id=\"fs-id3105099\"> a standard used for expressing and comparing measurements<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id2968885\">\n<dt>SI units <\/dt>\n<dd id=\"fs-id1577059\">the international system of units that scientists in most countries have agreed to use; includes units such as meters, liters, and grams<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id2582101\">\n<dt>English units<\/dt>\n<dd id=\"fs-id2018396\"> system of measurement used in the United States; includes units of measurement such as feet, gallons, and pounds<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id3401009\">\n<dt>fundamental units<\/dt>\n<dd id=\"fs-id2991354\"> units that can only be expressed relative to the procedure used to measure them<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id2512053\">\n<dt>derived units<\/dt>\n<dd id=\"fs-id3186991\"> units that can be calculated using algebraic combinations of the fundamental units<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id2771646\">\n<dt>second<\/dt>\n<dd id=\"fs-id3187001\"> the SI unit for time, abbreviated (s)<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id2910820\">\n<dt>meter<\/dt>\n<dd id=\"fs-id3201842\"> the SI unit for length, abbreviated (m)<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id2806926\">\n<dt>kilogram<\/dt>\n<dd id=\"fs-id2573988\"> the SI unit for mass, abbreviated (kg)<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id1990374\">\n<dt>metric system<\/dt>\n<dd id=\"fs-id2573998\"> a system in which values can be calculated in factors of 10<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id1950368\">\n<dt>order of magnitude<\/dt>\n<dd id=\"fs-id3348791\"> refers to the size of a quantity as it relates to a power of 10<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id2656746\">\n<dt>conversion factor<\/dt>\n<dd id=\"fs-id1434398\"> a ratio expressing how many of one unit are equal to another unit<\/dd>\n<\/dl>\n<\/div>\n","protected":false},"author":211,"menu_order":1,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"all-rights-reserved"},"chapter-type":[],"contributor":[],"license":[56],"class_list":["post-46","chapter","type-chapter","status-publish","hentry","license-all-rights-reserved"],"part":20,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters\/46","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/users\/211"}],"version-history":[{"count":1,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters\/46\/revisions"}],"predecessor-version":[{"id":47,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters\/46\/revisions\/47"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/parts\/20"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters\/46\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/media?parent=46"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapter-type?post=46"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/contributor?post=46"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/license?post=46"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}