{"id":1284,"date":"2018-04-11T22:51:06","date_gmt":"2018-04-12T02:51:06","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/chapter\/1-4-measurements\/"},"modified":"2018-06-22T22:57:21","modified_gmt":"2018-06-23T02:57:21","slug":"1-4-measurements","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/chapter\/1-4-measurements\/","title":{"raw":"2.2 Measurements and Units","rendered":"2.2 Measurements and Units"},"content":{"raw":"<div>\r\n<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Objectives<\/h3>\r\nBy the end of this section, you will be able to:\r\n<ul>\r\n \t<li>Explain the process of measurement<\/li>\r\n \t<li>Identify the three basic parts of a quantity<\/li>\r\n \t<li>Describe the properties and units of length, mass, volume, density, temperature, and time<\/li>\r\n \t<li>Perform basic unit calculations and conversions in the metric and other unit systems<\/li>\r\n<\/ul>\r\n<\/div>\r\nThe development of modern chemistry is often attributed to 18th century Frenchman Antoine-Laurent de Lavoisier, who was able though meticulous and careful scientific measurements that during a chemical reaction mass is neither consumed or created, the principle that led to <strong>the law of conservation of mass<\/strong>, one of the important fundamental principles in your study of chemistry. It is fundamentally important to realize that a science is for the most part a quantitative endeavor. Our ability to make observations through numerical measures is one of the cornerstones of the scientific method.\r\n<p id=\"fs-idm75764096\">Measurements provide the macroscopic information that is the basis of most of the hypotheses, theories, and laws that describe the behavior of matter and energy in both the macroscopic and microscopic domains of chemistry. Every measurement provides three kinds of information: a number (quantitative observation), a unit (describes how it was measured), and the degree of reliability (uncertainty of the measurement). While the number and unit are explicitly represented when a quantity is written, the uncertainty is an aspect of the measurement result that is more implicitly represented and will be discussed later.<\/p>\r\n<p id=\"fs-idm128012432\">The number in the measurement can be represented in different ways, including decimal form and scientific notation. For example, the maximum takeoff weight of a Boeing 777-200ER airliner is 298,000 kilograms, which can also be written as 2.98 \u00d7 10<sup>5<\/sup> kg. The mass of the average mosquito is about 0.0000025 kilograms, which can be written as 2.5 \u00d7 10<sup>\u22126<\/sup> kg.<\/p>\r\n<p id=\"fs-idp178656\"><strong>Units<\/strong>, such as liters, pounds, and centimeters, are standards of comparison for measurements. When we buy a 2-liter bottle of a soft drink, we expect that the volume of the drink was measured, so it is two times larger than the volume that everyone agrees to be 1 liter. The meat used to prepare a 0.25-pound hamburger is measured so it weighs one-fourth as much as 1 pound. Without units, a number can be meaningless, confusing, or possibly life threatening. Suppose a doctor prescribes phenobarbital to control a patient\u2019s seizures and states a dosage of \u201c100\u201d without specifying units. Not only will this be confusing to the medical professional giving the dose, but the consequences can be dire: 100 mg given three times per day can be effective as an anticonvulsant, but a single dose of 100 g is more than 10 times the lethal amount.<\/p>\r\n<p id=\"fs-idm144392592\">We usually report the results of scientific measurements in SI units, an updated version of the metric system, using the units listed in <a href=\"#fs-idm81346144\" class=\"autogenerated-content\">Table 1<\/a>. Other units can be derived from these base units. The standards for these units are fixed by international agreement, and they are called the <strong>International System of Units<\/strong> or <strong>SI Units<\/strong> (from the French, <em>Le Syst\u00e8me International d\u2019Unit\u00e9s<\/em>). SI units have been used by the United States National Institute of Standards and Technology (NIST) since 1964.<\/p>\r\n\r\n<table id=\"fs-idm81346144\" class=\"span-all\" summary=\"Length is measured with the meter, which is symbolized using a lowercase M. Mass is measured with the kilogram which is symbolized with a lowercase K G. Time is measured with the second, which is symbolized with a lowercase S. Temperature is measured with the kelvin which is symbolized with an uppercase K. Electric current is measured with the ampere which is symbolized with an uppercase A. The amount of a substance is measured with the mole, which is symbolized with the lowercase letters, M O L. Luminous intensity is measured with the candela, which is symbolized with the lowercase letters C D.\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th>Property Measured<\/th>\r\n<th>Name of Unit<\/th>\r\n<th>Symbol of Unit<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>length<\/td>\r\n<td>meter<\/td>\r\n<td>m<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>mass<\/td>\r\n<td>kilogram<\/td>\r\n<td>kg<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>time<\/td>\r\n<td>second<\/td>\r\n<td>s<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>temperature<\/td>\r\n<td>kelvin<\/td>\r\n<td>K<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>electric current<\/td>\r\n<td>ampere<\/td>\r\n<td>A<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>amount of substance<\/td>\r\n<td>mole<\/td>\r\n<td>mol<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>luminous intensity<\/td>\r\n<td>candela<\/td>\r\n<td>cd<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"3\"><strong>Table 1.<\/strong> Base Units of the SI System<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"eip-134\">Sometimes we use units that are fractions or multiples of a base unit. Ice cream is sold in quarts (a familiar, non-SI base unit), pints (0.5 quart), or gallons (4 quarts). We also use fractions or multiples of units in the SI system, but these fractions or multiples are always powers of 10. Fractional or multiple SI units are named using a prefix and the name of the base unit. For example, a length of 1000 meters is also called a kilometer because the prefix <em>kilo<\/em> means \u201cone thousand,\u201d which in scientific notation is 10<sup>3<\/sup> (1 kilometer = 1000 m = 10<sup>3<\/sup> m). The prefixes used and the powers to which 10 are raised are listed in <a href=\"#fs-idm81128320\" class=\"autogenerated-content\">Table 2<\/a>.<\/p>\r\n\r\n<div id=\"fs-idp86805728\" class=\"textbox shaded\">\r\n\r\n<img src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/CNX_Interactive_200DPI-1-2.png\" alt=\"\" width=\"122\" height=\"76\" class=\"alignleft\" \/>\r\n<p id=\"fs-idm169361696\">Need a refresher or more practice with scientific notation? Visit this <a href=\"http:\/\/openstaxcollege.org\/l\/16notation\">site<\/a> to go over the basics of scientific notation.<\/p>\r\n&nbsp;\r\n\r\n<\/div>\r\n<table id=\"fs-idm81128320\" class=\"span-all\" summary=\"The prefix femto has the symbol lowercase f and a factor of 10 to the negative fifteenth power. Therefore, 1 femtosecond, F S, is equal to 1 times 10 to the negative 15 of a meter, or 0.000000000001 of a meter. The prefix pico has the symbol lowercase P and a factor of 10 to the negative twelfth power. Therefore, 1 picosecond, P S, is equal to 1 times 10 to the negative 12 of a meter, or 0.000000000001 of a meter. The prefix nano has the symbol lowercase N and a factor of 10 to the negative ninth power. Therefore, 4 nanograms, or NG, equals 4 times ten to the negative 9, or 0.000000004 g. The prefix micro has the greek letter mu as its symbol and a factor of 10 to the negative sixth power. Therefore, 1 microliter, or mu L, is equal to one times ten to the negative 6 or 0.000001 L. The prefix milli has a lowercase M as its symbol and a factor of 10 to the negative third power. Therefore, 2 millimoles, or M mol, are equal to two times ten to the negative 3 or 0.002 mol. The prefix centi has a lowercase C as its symbol and a factor of 10 to the negative second power. Therefore, 7 centimeters, or C M, are equal to seven times ten to the negative 2 meters or 0.07 M O L. The prefix deci has a lowercase D as its symbol and a factor of 10 to the negative first power. Therefore, 1 deciliter, or lowercase D uppercase L, are equal to one times ten to the negative 1 meters or 0.1 L. The prefix kilo has a lowercase K as its symbol and a factor of 10 to the third power. Therefore, 1 kilometer, or K M, is equal to one times ten to the third meters or 1000 M. The prefix mega has an uppercase M as its symbol and a factor of 10 to the sixth power. Therefore, 3 megahertz, or M H Z, are equal to three times 10 to the sixth hertz, or 3000000 H Z. The prefix giga has an uppercase G as its symbol and a factor of 10 to the ninth power. Therefore, 8 gigayears, or G Y R, are equal to eight times 10 to the ninth years, or 800000000 G Y R. The prefix tera has an uppercase T as its symbol and a factor of 10 to the twelfth power. Therefore, 5 terawatts, or T W, are equal to five times 10 to the twelfth watts, or 5000000000000 W.\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th style=\"width: 45px\">Prefix<\/th>\r\n<th style=\"width: 56px\">Symbol<\/th>\r\n<th style=\"width: 49px\">Factor<\/th>\r\n<th style=\"width: 369px\">Example<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td style=\"width: 45px\">femto<\/td>\r\n<td style=\"width: 56px\">f<\/td>\r\n<td style=\"width: 49px\">10<sup>\u221215<\/sup><\/td>\r\n<td style=\"width: 369px\">1 femtosecond (fs) = 1 \u00d7 10<sup>\u221215<\/sup> s (0.000000000000001 s)<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"width: 45px\">pico<\/td>\r\n<td style=\"width: 56px\">p<\/td>\r\n<td style=\"width: 49px\">10<sup>\u221212<\/sup><\/td>\r\n<td style=\"width: 369px\">1 picometer (pm) = 1 \u00d7 10<sup>\u221212<\/sup> m (0.000000000001 m)<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"width: 45px\">nano<\/td>\r\n<td style=\"width: 56px\">n<\/td>\r\n<td style=\"width: 49px\">10<sup>\u22129<\/sup><\/td>\r\n<td style=\"width: 369px\">4 nanograms (ng) = 4 \u00d7 10<sup>\u22129<\/sup> g (0.000000004 g)<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"width: 45px\">micro<\/td>\r\n<td style=\"width: 56px\">\u00b5<\/td>\r\n<td style=\"width: 49px\">10<sup>\u22126<\/sup><\/td>\r\n<td style=\"width: 369px\">1 microliter (\u03bcL) = 1 \u00d7 10<sup>\u22126<\/sup> L (0.000001 L)<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"width: 45px\">milli<\/td>\r\n<td style=\"width: 56px\">m<\/td>\r\n<td style=\"width: 49px\">10<sup>\u22123<\/sup><\/td>\r\n<td style=\"width: 369px\">2 millimoles (mmol) = 2 \u00d7 10<sup>\u22123<\/sup> mol (0.002 mol)<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"width: 45px\">centi<\/td>\r\n<td style=\"width: 56px\">c<\/td>\r\n<td style=\"width: 49px\">10<sup>\u22122<\/sup><\/td>\r\n<td style=\"width: 369px\">7 centimeters (cm) = 7 \u00d7 10<sup>\u22122<\/sup> m (0.07 m)<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"width: 45px\">deci<\/td>\r\n<td style=\"width: 56px\">d<\/td>\r\n<td style=\"width: 49px\">10<sup>\u22121<\/sup><\/td>\r\n<td style=\"width: 369px\">1 deciliter (dL) = 1 \u00d7 10<sup>\u22121<\/sup> L (0.1 L )<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"width: 45px\">kilo<\/td>\r\n<td style=\"width: 56px\">k<\/td>\r\n<td style=\"width: 49px\">10<sup>3<\/sup><\/td>\r\n<td style=\"width: 369px\">1 kilometer (km) = 1 \u00d7 10<sup>3<\/sup> m (1000 m)<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"width: 45px\">mega<\/td>\r\n<td style=\"width: 56px\">M<\/td>\r\n<td style=\"width: 49px\">10<sup>6<\/sup><\/td>\r\n<td style=\"width: 369px\">3 megahertz (MHz) = 3 \u00d7 10<sup>6<\/sup> Hz (3,000,000 Hz)<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"width: 45px\">giga<\/td>\r\n<td style=\"width: 56px\">G<\/td>\r\n<td style=\"width: 49px\">10<sup>9<\/sup><\/td>\r\n<td style=\"width: 369px\">8 gigayears (Gyr) = 8 \u00d7 10<sup>9<\/sup> yr (8,000,000,000 Gyr)<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"width: 45px\">tera<\/td>\r\n<td style=\"width: 56px\">T<\/td>\r\n<td style=\"width: 49px\">10<sup>12<\/sup><\/td>\r\n<td style=\"width: 369px\">5 terawatts (TW) = 5 \u00d7 10<sup>12<\/sup> W (5,000,000,000,000 W)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 519px\" colspan=\"4\"><strong>Table 2.<\/strong> Common Unit Prefixes<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<section id=\"fs-idp25374912\">\r\n<h2>SI Base Units<\/h2>\r\n<p id=\"fs-idp389936\">The initial units of the metric system, which eventually evolved into the SI system, were established in France during the French Revolution. The original standards for the meter and the kilogram were adopted there in 1799 and eventually by other countries. This section introduces four of the SI base units commonly used in chemistry. Other SI units will be introduced in subsequent chapters.<\/p>\r\n\r\n<section id=\"fs-idp679312\">\r\n<h2>Length<\/h2>\r\n<p id=\"fs-idm64613648\">The standard unit of <strong>length<\/strong> in both the SI and original metric systems is the <strong>meter (m)<\/strong>. A meter was originally specified as 1\/10,000,000 of the distance from the North Pole to the equator. It is now defined as the distance light in a vacuum travels in 1\/299,792,458 of a second. A meter is about 3 inches longer than a yard (<a href=\"#CNX_Chem_01_04_MYdCmIn\" class=\"autogenerated-content\">Figure 1<\/a>); one meter is about 39.37 inches or 1.094 yards. Longer distances are often reported in kilometers (1 km = 1000 m = 10<sup>3<\/sup> m), whereas shorter distances can be reported in centimeters (1 cm = 0.01 m = 10<sup>\u22122<\/sup> m) or millimeters (1 mm = 0.001 m = 10<sup>\u22123<\/sup> m).<\/p>\r\n\r\n<figure id=\"CNX_Chem_01_04_MYdCmIn\">\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"1300\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/CNX_Chem_01_04_MYdCmIn-2.jpg\" alt=\"One meter is slightly larger than a yard and one centimeter is less than half the size of one inch. 1 inch is equal to 2.54 cm. 1 m is equal to 1.094 yards which is equal to 39.36 inches.\" width=\"1300\" height=\"639\" \/> <strong>Figure 1.<\/strong> The relative lengths of 1 m, 1 yd, 1 cm, and 1 in. are shown (not actual size), as well as comparisons of 2.54 cm and 1 in., and of 1 m and 1.094 yd.[\/caption]<\/figure>\r\n<\/section><section id=\"fs-idm1313360\">\r\n<h2>Mass<\/h2>\r\n<p id=\"fs-idp222999216\">The standard unit of mass in the SI system is the <strong>kilogram (kg)<\/strong>. A kilogram was originally defined as the mass of a liter of water (a cube of water with an edge length of exactly 0.1 meter). It is now defined by a certain cylinder of platinum-iridium alloy, which is kept in France (<a href=\"#CNX_Chem_01_04_Kilogram\" class=\"autogenerated-content\">Figure 2<\/a>). Any object with the same mass as this cylinder is said to have a mass of 1 kilogram. One kilogram is about 2.2 pounds. The gram (g) is exactly equal to 1\/1000 of the mass of the kilogram (10<sup>\u22123<\/sup> kg).<\/p>\r\n\r\n<figure id=\"CNX_Chem_01_04_Kilogram\">\r\n\r\n[caption id=\"attachment_1282\" align=\"aligncenter\" width=\"200\"]<a href=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/CNX_Chem_01_04_Kilogram-2-e1528931146214.jpg\"><img src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/CNX_Chem_01_04_Kilogram-2-e1528931146214.jpg\" alt=\"\" width=\"200\" height=\"283\" class=\"wp-image-1282 size-full\" \/><\/a> <strong>Figure 2.<\/strong> This replica prototype kilogram is housed at the National Institute of Standards and Technology (NIST) in Maryland. (credit: National Institutes of Standards and Technology)[\/caption]<\/figure>\r\n<\/section><section id=\"fs-idm1531808\">\r\n<h2>Temperature<\/h2>\r\n<p id=\"fs-idp3379184\">Temperature is an intensive property. The SI unit of temperature is the <strong>kelvin (K)<\/strong>. The IUPAC convention is to use kelvin (all lowercase) for the word, K (uppercase) for the unit symbol, and neither the word \u201cdegree\u201d nor the degree symbol (\u00b0). The degree <strong>Celsius (\u00b0C)<\/strong> is also allowed in the SI system, with both the word \u201cdegree\u201d and the degree symbol used for Celsius measurements. Celsius degrees are the same magnitude as those of kelvin, but the two scales place their zeros in different places. Water freezes at 273.15 K (0 \u00b0C) and boils at 373.15 K (100 \u00b0C) by definition, and normal human body temperature is approximately 310 K (37 \u00b0C). The conversion between these two units and the Fahrenheit scale will be discussed later in this chapter.<\/p>\r\n\r\n<\/section><section id=\"fs-idm101578432\">\r\n<h2>Time<\/h2>\r\n<p id=\"fs-idm101738864\">The SI base unit of time is the <strong>second (s)<\/strong>. Small and large time intervals can be expressed with the appropriate prefixes; for example, 3 microseconds = 0.000003 s = 3 \u00d7 10<sup>\u22126<\/sup> and 5 megaseconds = 5,000,000 s = 5 \u00d7 10<sup>6<\/sup> s. Alternatively, hours, days, and years can be used.<\/p>\r\n\r\n<\/section><\/section><section id=\"fs-idm23668768\">\r\n<h2>Derived SI Units<\/h2>\r\n<p id=\"fs-idm10854912\">We can derive many units from the seven SI base units. For example, we can use the base unit of length to define a unit of volume, and the base units of mass and length to define a unit of density.<\/p>\r\n\r\n<section id=\"fs-idm16046736\">\r\n<h2>Volume<\/h2>\r\n<p id=\"fs-idm77137776\"><strong>Volume<\/strong> is the measure of the amount of space occupied by an object. The standard SI unit of volume is defined by the base unit of length (<a href=\"#CNX_Chem_01_04_Volume\" class=\"autogenerated-content\">Figure 3<\/a>). The standard volume is a <strong>cubic meter (m<sup>3<\/sup>)<\/strong>, a cube with an edge length of exactly one meter. To dispense a cubic meter of water, we could build a cubic box with edge lengths of exactly one meter. This box would hold a cubic meter of water or any other substance.<\/p>\r\n<p id=\"fs-idm81813264\">A more commonly used unit of volume is derived from the decimeter (0.1 m, or 10 cm). A cube with edge lengths of exactly one decimeter contains a volume of one cubic decimeter (dm<sup>3<\/sup>). A <strong>liter (L) <\/strong> is the more common name for the cubic decimeter. One liter is about 1.06 quarts.<\/p>\r\n<p id=\"fs-idm163691744\">A <strong>cubic centimeter (cm<sup>3<\/sup>)<\/strong> is the volume of a cube with an edge length of exactly one centimeter. The abbreviation <strong>cc<\/strong> (for <strong>c<\/strong>ubic <strong>c<\/strong>entimeter) is often used by health professionals. A cubic centimeter is also called a <strong>milliliter (mL)<\/strong> and is 1\/1000 of a liter.<\/p>\r\n\r\n<figure id=\"CNX_Chem_01_04_Volume\">\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"1200\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/CNX_Chem_01_04_Volume-2.jpg\" alt=\"Figure A shows a large cube, which has a volume of 1 meter cubed. This larger cube is made up of many smaller cubes in a 10 by 10 pattern. Each of these smaller cubes has a volume of 1 decimeter cubed, or one liter. Each of these smaller cubes is, in turn, made up of many tiny cubes. Each of these tiny cubes has a volume of 1 centimeter cubed, or one milliliter. A one cubic centimeter cube is about the same width as a dime, which has a width of 1.8 centimeter.\" width=\"1200\" height=\"675\" \/> <strong>Figure 3<\/strong> (a) The relative volumes are shown for cubes of 1 m<sup>3<\/sup>, 1 dm<sup>3<\/sup> (1 L), and 1 cm<sup>3<\/sup> (1 mL) (not to scale). (b) The diameter of a dime is compared relative to the edge length of a 1-cm<sup>3<\/sup> (1-mL) cube.[\/caption]<\/figure>\r\n<\/section><section id=\"fs-idm18447104\">\r\n<h2>Density<\/h2>\r\n<p id=\"fs-idp205372288\">We use the mass and volume of a substance to determine its density. Thus, the units of density are defined by the base units of mass and length.<\/p>\r\n<p id=\"fs-idm74744496\">The <strong>density<\/strong> of a substance is the ratio of the mass of a sample of the substance to its volume. The SI unit for density is the kilogram per cubic meter (kg\/m<sup>3<\/sup>). For many situations, however, this as an inconvenient unit, and we often use grams per cubic centimeter (g\/cm<sup>3<\/sup>) for the densities of solids and liquids, and grams per liter (g\/L) for gases. Although there are exceptions, most liquids and solids have densities that range from about 0.7 g\/cm<sup>3<\/sup> (the density of gasoline) to 19 g\/cm<sup>3<\/sup> (the density of gold). The density of air is about 1.2 g\/L. <a href=\"#fs-idm45639696\" class=\"autogenerated-content\">Table 3<\/a> shows the densities of some common substances.<\/p>\r\n\r\n<table id=\"fs-idm45639696\" class=\"span-all\" summary=\"This table reports the density of solids, liquids, and gases in grams per centimeters cubed. The values for solids are ice 0.92, oak wood 0.60 to 0.90, iron 7.9, copper 9.0, lead 11.3, silver 10.5, and gold 19.3. The values for liquids are water 1.0, ethanol 0.79, acetone 0.79, glycerin 1.26, olive oil 0.92, gasoline 0.70 to 0.77, and Mercury 13.6. The values for gases, which were measured when the gas was at 25 degrees Celsius and 1 atmosphere, are dry air 1.20, oxygen 1.31, nitrogen 1.14, carbon dioxide 1.80, helium 0.16, neon 0.83, and radon 9.1.\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th>Solids<\/th>\r\n<th>Liquids<\/th>\r\n<th>Gases (at 25 \u00b0C and 1 atm)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>ice (at 0 \u00b0C) 0.92 g\/cm<sup>3<\/sup><\/td>\r\n<td>water 1.0 g\/cm<sup>3<\/sup><\/td>\r\n<td>dry air 1.20 g\/L<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>oak (wood) 0.60\u20130.90 g\/cm<sup>3<\/sup><\/td>\r\n<td>ethanol 0.79 g\/cm<sup>3<\/sup><\/td>\r\n<td>oxygen 1.31 g\/L<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>iron 7.9 g\/cm<sup>3<\/sup><\/td>\r\n<td>acetone 0.79 g\/cm<sup>3<\/sup><\/td>\r\n<td>nitrogen 1.14 g\/L<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>copper 9.0 g\/cm<sup>3<\/sup><\/td>\r\n<td>glycerin 1.26 g\/cm<sup>3<\/sup><\/td>\r\n<td>carbon dioxide 1.80 g\/L<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>lead 11.3 g\/cm<sup>3<\/sup><\/td>\r\n<td>olive oil 0.92 g\/cm<sup>3<\/sup><\/td>\r\n<td>helium 0.16 g\/L<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>silver 10.5 g\/cm<sup>3<\/sup><\/td>\r\n<td>gasoline 0.70\u20130.77 g\/cm<sup>3<\/sup><\/td>\r\n<td>neon 0.83 g\/L<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>gold 19.3 g\/cm<sup>3<\/sup><\/td>\r\n<td>mercury 13.6 g\/cm<sup>3<\/sup><\/td>\r\n<td>radon 9.1 g\/L<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"3\"><strong>Table 3.<\/strong> Densities of Common Substances<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-idm81523280\">While there are many ways to determine the density of an object, perhaps the most straightforward method involves separately finding the mass and volume of the object, and then dividing the mass of the sample by its volume. In the following example, the mass is found directly by weighing, but the volume is found indirectly through length measurements.<\/p>\r\n\r\n<div class=\"equation\" id=\"fs-idm166517584\" style=\"text-align: center\">$latex \\text{density} = \\frac{\\text{mass}}{\\text{volume}} $<\/div>\r\n<\/section>\r\n<div class=\"textbox shaded\" id=\"Example_01_04_01\">\r\n<h3>Example 1<\/h3>\r\nGold\u2014in bricks, bars, and coins\u2014has been a form of currency for centuries. In order to swindle people into paying for a brick of gold without actually investing in a brick of gold, people have considered filling the centers of hollow gold bricks with lead to fool buyers into thinking that the entire brick is gold. It does not work: Lead is a dense substance, but its density is not as great as that of gold, 19.3 g\/cm<sup>3<\/sup>. What is the density of lead if a cube of lead has an edge length of 2.00 cm and a mass of 90.7 g?\r\n\r\n&nbsp;\r\n<p id=\"fs-idp40298832\"><strong>Solution<\/strong>\r\nThe density of a substance can be calculated by dividing its mass by its volume. The volume of a cube is calculated by cubing the edge length.<\/p>\r\n<p style=\"text-align: center\">$latex \\text{volume of lead cube}=2.00\\text{cm}\\times2.00\\text{cm}\\times2.00\\text{cm}=9.00\\text{cm}^3 $<\/p>\r\n<p style=\"text-align: center\">$latex \\text{density}=\\frac{\\text{mass}}{\\text{volume}}=\\frac{90.7\\text{g}}{8.00\\text{cm}^3}=\\frac{11.3\\text{g}}{1.00\\text{cm}^3}=11.3\\;\\text{g}\/\\text{cm}^3 $<\/p>\r\n\r\n<div class=\"example\">\r\n<div class=\"equation\" id=\"fs-idm163080256\" style=\"text-align: center\"><\/div>\r\n<p id=\"fs-idp264752\">(We will discuss the reason for rounding to the first decimal place in the next section.)<\/p>\r\n&nbsp;\r\n<p id=\"fs-idp2742064\"><strong><em>Test Yourself<\/em><\/strong>\r\na) To three decimal places, what is the volume of a cube (cm<sup>3<\/sup>) with an edge length of 0.843 cm?<\/p>\r\n<p id=\"fs-idp116749488\">b) If the cube in part a) is copper and has a mass of 5.34 g, what is the density of copper to two decimal places?<\/p>\r\n&nbsp;\r\n\r\n<strong><em>Answers<\/em><\/strong>\r\n\r\na) 0.599 cm<sup>3<\/sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 b) 8.91 g\/cm<sup>3<\/sup>\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idm83823632\" class=\"textbox shaded\">\r\n\r\n<img src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/CNX_Interactive_200DPI-1-2.png\" alt=\"\" width=\"129\" height=\"80\" class=\"alignleft\" \/>\r\n\r\n&nbsp;\r\n<p id=\"fs-idm108028240\">To learn more about the relationship between mass, volume, and density, use this <a href=\"http:\/\/openstaxcollege.org\/l\/16phetmasvolden\">interactive simulator<\/a> to explore the density of different materials, like wood, ice, brick, and aluminum.<\/p>\r\n\r\n<\/div>\r\n<div class=\"textbox shaded\" id=\"Example_01_04_02\">\r\n<h3>Example 2<\/h3>\r\n<p id=\"fs-idm108240880\">This <a href=\"http:\/\/openstaxcollege.org\/l\/16phetmasvolden\">PhET simulation<\/a> illustrates another way to determine density, using displacement of water. Determine the density of the red and yellow blocks.<\/p>\r\n&nbsp;\r\n<p id=\"fs-idp206606992\"><strong>Solution<\/strong>\r\nWhen you open the density simulation and select Same Mass, you can choose from several 5.00-kg colored blocks that you can drop into a tank containing 100.00 L water. The yellow block floats (it is less dense than water), and the water level rises to 105.00 L. While floating, the yellow block displaces 5.00 L water, an amount equal to the weight of the block. The red block sinks (it is more dense than water, which has density = 1.00 kg\/L), and the water level rises to 101.25 L.<\/p>\r\n<p id=\"fs-idm85356448\">The red block therefore displaces 1.25 L water, an amount equal to the volume of the block. The density of the red block is:<\/p>\r\n\r\n<div class=\"equation\" id=\"fs-idm94054304\" style=\"text-align: center\">$latex \\text{density}=\\frac{\\text{mass}}{\\text{volume}}=\\frac{5.00\\;\\text{kg}}{1.25\\;\\text{L}}=4.00 \\text{kg\/L} $<\/div>\r\n<p id=\"fs-idm92012848\">Note that since the yellow block is not completely submerged, you cannot determine its density from this information. But if you hold the yellow block on the bottom of the tank, the water level rises to 110.00 L, which means that it now displaces 10.00 L water, and its density can be found:<\/p>\r\n\r\n<div class=\"equation\" id=\"fs-idm174274016\">\r\n<p style=\"text-align: center\">$latex \\text{density}=\\frac{\\text{mass}}{\\text{volume}}=\\frac{\\text{5.00 kg}}{\\text{10.00 L}}=0.500 \\text{kg\/L} $<\/p>\r\n&nbsp;\r\n<p id=\"fs-idp10631184\" style=\"text-align: left\"><strong><em>Test Yourself<\/em><\/strong>\r\nRemove all of the blocks from the water and add the green block to the tank of water, placing it approximately in the middle of the tank. Determine the density of the green block.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: left\"><strong><em>Answer<\/em><\/strong><\/p>\r\n<p style=\"text-align: left\">2.00 kg\/L<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n<div class=\"textbox shaded\">\r\n<div class=\"callout block\" id=\"ball-ch03_n01\">\r\n<h3><strong>The Angstrom Unit<\/strong><\/h3>\r\n<p class=\"title\">Although not an SI unit, the angstrom (\u00c5) is a useful unit of length. It is one ten-billionth of a meter, or 10<sup class=\"superscript\">\u221210<\/sup>\u00a0m. Why is it a useful unit? The ultimate particles that compose all matter are about 10<sup class=\"superscript\">\u221210<\/sup> m in size, or about 1 \u00c5. This makes the angstrom a natural\u2014though not approved\u2014unit for describing these particles.<\/p>\r\n<p id=\"ball-ch03_p02\" class=\"para\">The angstrom unit is named after Anders Jonas \u00c5ngstr\u00f6m, a nineteenth-century Swedish physicist. \u00c5ngstr\u00f6m\u2019s research dealt with light being emitted by glowing objects, including the sun. \u00c5ngstr\u00f6m studied the brightness of the different colors of light that the sun emitted and was able to deduce that the sun is composed of the same kinds of matter that are present on the earth. By extension, we now know that all matter throughout the universe is similar to the matter that exists on our own planet.<\/p>\r\n<p class=\"para\"><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/09\/The-Sun.png\"><img src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/The-Sun-1.png\" alt=\"The Sun\" width=\"400\" height=\"229\" class=\"wp-image-4624 aligncenter\" \/><\/a><\/p>\r\n\r\n<div class=\"informalfigure large\" id=\"ball-ch03_f01\">\r\n<p class=\"para\">Anders Jonas \u00c5ngstrom, a Swedish physicist, studied the light coming from the sun. His contributions to science were sufficient to have a tiny unit of length named after him, the angstrom, which is one ten-billionth of a meter.<\/p>\r\n\r\n<div class=\"copyright\">\r\n<p class=\"para\">Source: Photo of the sun courtesy of NASA\u2019s Solar Dynamics Observatory, <a class=\"link\" href=\"http:\/\/commons.wikimedia.org\/wiki\/File:The_Sun_by_the_Atmospheric_Imaging_Assembly_of_NASA%27s_Solar_Dynamics_Observatory_-_20100801.jpg\" target=\"_blank\" rel=\"noopener\">http:\/\/commons.wikimedia.org\/wiki\/File:The_Sun_by_the_Atmospheric_Imaging_Assembly_of_NASA%27s_Solar_Dynamics_Observatory_-_20100801.jpg<\/a>.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div><section id=\"fs-idm333536464\" class=\"summary\">\r\n<h2>Key Concepts and Summary<\/h2>\r\n<p id=\"fs-idm330017088\">Measurements provide quantitative information that is critical in studying and practicing chemistry. Each measurement has an amount, a unit for comparison, and an uncertainty. Measurements can be represented in either decimal or scientific notation. Scientists primarily use the SI (International System) or metric systems. We use base SI units such as meters, seconds, and kilograms, as well as derived units, such as liters (for volume) and g\/cm<sup>3<\/sup> (for density). In many cases, we find it convenient to use unit prefixes that yield fractional and multiple units, such as microseconds (10<sup>\u22126<\/sup> seconds) and megahertz (10<sup>6<\/sup> hertz), respectively.<\/p>\r\n\r\n<\/section><section id=\"fs-idm313032912\" class=\"key-equations\">\r\n<h2>Key Equations<\/h2>\r\n<ul id=\"fs-idm76167888\">\r\n \t<li>$latex \\text{density}=\\frac{\\text{mass}}{\\text{volume}} $<\/li>\r\n<\/ul>\r\n<div class=\"textbox examples\">\r\n<h3 itemprop=\"educationalUse\">Activity<\/h3>\r\nMake yourself a stack of small sized Qcards to help you learn your common unit prefixes, which is important because you will use later as conversion factors for unit conversions. \u00a0On one side have the common unit prefix associated with a base unit (e.g. 1 kg) and on the other side have its equivalence in terms of the base unit (e.g. 10<sup>3<\/sup> g). \u00a0Make a complete set of using all the common unit prefixes from Table 2 and pick and choose different base units from Table 1. \u00a0Then use these Qcards to quiz yourself.\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Exercises<\/h3>\r\n<div class=\"question\">\r\n<p id=\"ball-ch02_s02_qs01_p1\" class=\"para\">1. \u00a0Identify the unit in each quantity.<\/p>\r\n\r\n<\/div>\r\na) \u00a02 boxes of crayons \u00a0 \u00a0\u00a0b) \u00a03.5 grams of gold\r\n<div class=\"question\">\r\n<p id=\"ball-ch02_s02_qs01_p2\" class=\"para\">2. \u00a0Identify the unit in each quantity.<\/p>\r\na) \u00a032 oz of cheddar cheese \u00a0 \u00a0\u00a0b) \u00a00.045 cm<sup class=\"superscript\">3<\/sup> of water<span style=\"font-size: 1em\">\u00a0<\/span>\r\n\r\n<\/div>\r\n<div class=\"question\">\r\n<p id=\"ball-ch02_s02_qs01_p3\" class=\"para\">3. \u00a0Identify the unit in each quantity.<\/p>\r\na) \u00a09.58 s (the current world record in the 100 m dash)\r\n\r\nb) \u00a06.14 m (the current world record in the pole vault)\r\n\r\n<\/div>\r\n<div class=\"question\">\r\n<p id=\"ball-ch02_s02_qs01_p4\" class=\"para\">4. \u00a0Identify the unit in each quantity.<\/p>\r\na) \u00a02 dozen eggs\r\n\r\nb) \u00a02.4 km\/s (the escape velocity of the moon, which is the velocity you need at the surface to escape the moon\u2019s gravity)\r\n\r\n<\/div>\r\n<div class=\"question\">\r\n<p id=\"ball-ch02_s02_qs01_p5\" class=\"para\">5. \u00a0Indicate what multiplier each prefix represents.<\/p>\r\na) \u00a0k \u00a0 \u00a0\u00a0b) \u00a0m \u00a0 \u00a0\u00a0c) \u00a0M\r\n\r\n<\/div>\r\n<div class=\"question\">\r\n<p id=\"ball-ch02_s02_qs01_p6\" class=\"para\">6. \u00a0Indicate what multiplier each prefix represents.<\/p>\r\na) \u00a0c \u00a0 \u00a0\u00a0b) \u00a0G \u00a0 \u00a0\u00a0c) \u00a0\u03bc\r\n\r\n<\/div>\r\n<span style=\"font-size: 1em\">7. \u00a0Give the prefix that represents each multiplier.<\/span>\r\n<div class=\"question\">\r\n\r\na) \u00a01\/1,000th \u00d7 \u00a0 \u00a0\u00a0b) \u00a01,000 \u00d7 \u00a0 \u00a0 \u00a0c) \u00a01,000,000,000 \u00d7\r\n\r\n<\/div>\r\n<div class=\"question\">\r\n<p id=\"ball-ch02_s02_qs01_p8\" class=\"para\">8. \u00a0Give the prefix that represents each multiplier.<\/p>\r\na) \u00a01\/1,000,000,000th \u00d7 \u00a0 \u00a0\u00a0b) \u00a01\/100th \u00d7 \u00a0 \u00a0\u00a0c) \u00a01,000,000 \u00d7\r\n\r\n&nbsp;\r\n\r\n9. Complete the following table with the missing information.\r\n\r\n<\/div>\r\n<div class=\"question\">\r\n<div class=\"informaltable\">\r\n<table style=\"border-color: #000000;border-spacing: 0px\" cellpadding=\"0\">\r\n<thead>\r\n<tr>\r\n<th>Unit<\/th>\r\n<th align=\"center\">Abbreviation<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>kilosecond<\/td>\r\n<td align=\"center\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td align=\"center\">mL<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td align=\"center\">Mg<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>centimeter<\/td>\r\n<td align=\"center\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"question\">\r\n<p id=\"ball-ch02_s02_qs01_p10\" class=\"para\">10.Complete the following table with the missing information.<\/p>\r\n\r\n<div class=\"informaltable\">\r\n<table style=\"border-color: #000000;border-spacing: 0px\" cellpadding=\"0\">\r\n<thead>\r\n<tr>\r\n<th>Unit<\/th>\r\n<th align=\"center\">Abbreviation<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>kilometer per second<\/td>\r\n<td align=\"center\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>second<\/td>\r\n<td align=\"center\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td align=\"center\">cm<sup class=\"superscript\">3<\/sup><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td align=\"center\">\u03bcL<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>nanosecond<\/td>\r\n<td align=\"center\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n\r\n11. \u00a0Express each quantity in a more appropriate unit. There may be more than one acceptable answer.\r\n\r\n<\/div>\r\n<\/div>\r\na) \u00a03.44 \u00d7 10<sup class=\"superscript\">\u22126<\/sup> s \u00a0 \u00a0\u00a0b) \u00a03,500 L \u00a0 \u00a0\u00a0c) \u00a00.045 m\r\n\r\n<span style=\"font-size: 1em\">12. \u00a0Express each quantity in a more appropriate unit. There may be more than one acceptable answer.<\/span>\r\n<div class=\"question\">\r\n\r\na) \u00a00.000066 m\/s (Hint: you need consider only the unit in the numerator.)\r\n\r\nb) \u00a04.66 \u00d7 10<sup class=\"superscript\">6<\/sup> s\r\n\r\nc) \u00a07,654 L\r\n\r\n<\/div>\r\n<span style=\"font-size: 1em\">13. \u00a0Express each quantity in a more appropriate unit. There may be more than one acceptable answer.<\/span>\r\n<div class=\"question\">\r\n\r\na) \u00a043,600 mL \u00a0 \u00a0\u00a0b) \u00a00.0000044 m \u00a0 \u00a0\u00a0c) \u00a01,438 ms\r\n\r\n<\/div>\r\n<span style=\"font-size: 1em\">14. \u00a0Express each quantity in a more appropriate unit. There may be more than one acceptable answer.<\/span>\r\n<div class=\"question\">\r\n\r\na) \u00a00.000000345 m<sup class=\"superscript\">3 \u00a0 \u00a0\u00a0<\/sup>b) \u00a047,000,000 mm<sup class=\"superscript\">3 \u00a0 \u00a0\u00a0<\/sup>c) \u00a00.00665 L\r\n\r\n<\/div>\r\n<span style=\"font-size: 1em\">15. \u00a0Multiplicative prefixes are used for other units as well, such as computer memory. The basic unit of computer memory is the byte (b). What is the unit for one million bytes?<\/span>\r\n\r\n<span style=\"font-size: 1em\">16. \u00a0You may have heard the terms <\/span><em class=\"emphasis\" style=\"font-size: 1em\">microscale<\/em><span style=\"font-size: 1em\"> or <\/span><em class=\"emphasis\" style=\"font-size: 1em\">nanoscale<\/em><span style=\"font-size: 1em\"> to represent the sizes of small objects. What units of length do you think are useful at these scales? What fractions of the fundamental unit of length are these units?<\/span>\r\n\r\n<span style=\"font-size: 1em\">17. \u00a0Acceleration is defined as a change in velocity per time. Propose a unit for acceleration in terms of the fundamental SI units.<\/span>\r\n\r\n<span style=\"font-size: 1em\">18. \u00a0Density is defined as the mass of an object divided by its volume. Propose a unit of density in terms of the fundamental SI units.<\/span>\r\n<div class=\"question\">\r\n<p class=\"para\"><span style=\"font-size: 1em\">19. \u00a0Is a meter about an inch, a foot, a yard, or a mile?<\/span><\/p>\r\n<p class=\"para\"><span style=\"font-size: 1em\">20. \u00a0Indicate the SI base units or derived units that are appropriate for the following measurements:<\/span><\/p>\r\n\r\n<\/div>\r\n<p id=\"fs-idm270779504\">a) the mass of the moon<\/p>\r\n<p id=\"fs-idm7152592\">b) the distance from Dallas to Oklahoma City<\/p>\r\n<p id=\"fs-idm241075344\">c) the speed of sound<\/p>\r\n<p id=\"fs-idm11255792\">d) the density of air<\/p>\r\n<p id=\"fs-idm386910128\">e) the temperature at which alcohol boils<\/p>\r\n<p id=\"fs-idm312450912\">f) the area of the state of Delaware<\/p>\r\n<p id=\"fs-idm332809616\">g) the volume of a flu shot or a measles vaccination<\/p>\r\n21. \u00a0Give the name of the prefix and the quantity indicated by the following symbols that are used with SI base units.\r\n<p id=\"fs-idm184430352\">a) c \u00a0 \u00a0\u00a0b) d \u00a0 \u00a0\u00a0c) G \u00a0 \u00a0\u00a0d) k \u00a0 \u00a0\u00a0e) m \u00a0 \u00a0\u00a0f) n \u00a0 \u00a0 \u00a0g) p \u00a0 \u00a0\u00a0h) T<\/p>\r\n22. \u00a0Visit this <a href=\"http:\/\/openstaxcollege.org\/l\/16phetmasvolden\">PhET density simulation<\/a> and select the Same Volume Blocks.\r\n<p id=\"fs-idm148389344\">a) What are the mass, volume, and density of the yellow block?<\/p>\r\n<p id=\"fs-idm329801072\">b) What are the mass, volume and density of the red block?<\/p>\r\n<p id=\"fs-idm344699344\">c) List the block colors in order from smallest to largest mass.<\/p>\r\n<p id=\"fs-idm338418880\">d) List the block colors in order from lowest to highest density.<\/p>\r\n<p id=\"fs-idm310048112\">e) How are mass and density related for blocks of the same volume?<\/p>\r\n23. \u00a0Visit this <a href=\"http:\/\/openstaxcollege.org\/l\/16phetmasvolden\">PhET density simulation<\/a> and select Mystery Blocks.\r\n<p id=\"fs-idm153136896\">a) Pick one of the Mystery Blocks and determine its mass, volume, density, and its likely identity.<\/p>\r\n<p id=\"fs-idm127620640\">b) Pick a different Mystery Block and determine its mass, volume, density, and its likely identity.<\/p>\r\n<p id=\"fs-idm178736144\">c) Order the Mystery Blocks from least dense to most dense. Explain.<\/p>\r\n&nbsp;\r\n\r\n<b>Answers<\/b>\r\n\r\n1.\u00a0a) \u00a0boxes of crayons \u00a0 \u00a0\u00a0b) \u00a0grams of gold\r\n<p id=\"ball-ch02_s02_qs01_p2\" class=\"para\">2. \u00a0a) \u00a0oz of cheddar cheese \u00a0 \u00a0\u00a0b) cm<sup class=\"superscript\">3<\/sup> of water<\/p>\r\n3. \u00a0a) \u00a0seconds \u00a0 \u00a0\u00a0b) \u00a0meters\r\n<p id=\"ball-ch02_s02_qs01_p4\" class=\"para\">4. \u00a0a) \u00a0dozen of eggs \u00a0 \u00a0\u00a0b) \u00a0km\/s<\/p>\r\n5. \u00a0a) \u00a01,000 \u00d7 \u00a0 \u00a0 b) \u00a01\/1,000 \u00d7 \u00a0 \u00a0\u00a0c) \u00a01,000,000 \u00d7\r\n<div class=\"question\">\r\n<p id=\"ball-ch02_s02_qs01_p6\" class=\"para\">6. \u00a0a) \u00a01\/100 x \u00a0 \u00a0 b) 1,000,000,000 x \u00a0 \u00a0 c) 1\/1,000,000 x<\/p>\r\n\r\n<\/div>\r\n7. \u00a0a) \u00a0milli- \u00a0 \u00a0\u00a0b) \u00a0kilo- \u00a0 \u00a0\u00a0c) \u00a0giga-\r\n<p id=\"ball-ch02_s02_qs01_p8\" class=\"para\">8. \u00a0a) \u00a0nano- \u00a0 \u00a0\u00a0b) \u00a0centi- \u00a0 \u00a0\u00a0c) \u00a0mega-<\/p>\r\n9.\r\n<div class=\"informaltable\">\r\n<table style=\"border-color: #000000;border-spacing: 0px\" cellpadding=\"0\">\r\n<thead>\r\n<tr>\r\n<th>Unit<\/th>\r\n<th align=\"center\">Abbreviation<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>kilosecond<\/td>\r\n<td align=\"center\">ks<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>milliliter<\/td>\r\n<td align=\"center\">mL<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>megagram<\/td>\r\n<td align=\"center\">Mg<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>centimeter<\/td>\r\n<td align=\"center\">cm<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p id=\"ball-ch02_s02_qs01_p10\" class=\"para\">10.<\/p>\r\n\r\n<div class=\"informaltable\">\r\n<table style=\"border-color: #000000;border-spacing: 0px\" cellpadding=\"0\">\r\n<thead>\r\n<tr>\r\n<th>Unit<\/th>\r\n<th align=\"center\">Abbreviation<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>kilometer per second<\/td>\r\n<td align=\"center\">\u00a0km\/s<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>second<\/td>\r\n<td align=\"center\">s<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>\u00a0cubic centimeter<\/td>\r\n<td align=\"center\">cm<sup class=\"superscript\">3<\/sup><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>\u00a0microliter<\/td>\r\n<td align=\"center\">\u03bcL<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>nanosecond<\/td>\r\n<td align=\"center\">ns<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n11. \u00a0a) \u00a03.44 \u03bcs \u00a0 \u00a0\u00a0b) \u00a03.5 kL \u00a0 \u00a0\u00a0c) \u00a04.5 cm\r\n\r\n12. \u00a0a) 66 \u00b5m\/s \u00a0 \u00a0 b) 4.66 Ms \u00a0 \u00a0 c) 7.654 kL\r\n\r\n13. \u00a0a) \u00a043.6 L \u00a0 \u00a0\u00a0b) \u00a04.4 \u00b5m \u00a0 \u00a0\u00a0c) \u00a01.438 s\r\n\r\n14. \u00a0a) 345 mm<sup class=\"superscript\">3<\/sup> \u00a0 \u00a0 b) 47 dm<sup class=\"superscript\">3<\/sup> \u00a0 \u00a0 c) 6.65 mL\r\n\r\n15. megabytes (Mb)\r\n\r\n16. \u00a0<i>microscale =\u00a0\u00b5<\/i>m, 1\/1,000,000 \u00a0 \u00a0 \u00a0\u00a0<em>nanoscale =\u00a0<\/em>nm, 1\/1,000,000,000\r\n\r\n17. meters\/second<sup class=\"superscript\">2<\/sup>\r\n\r\n18. kg\/m<sup class=\"superscript\">3<\/sup>\r\n<p id=\"fs-idm339638512\">19. about a yard<\/p>\r\n<p id=\"fs-idm123011200\">20. a) kilograms \u00a0 \u00a0 \u00a0b) meters \u00a0 \u00a0 \u00a0c) kilometers\/second \u00a0 \u00a0 \u00a0d) kilograms\/cubic meter \u00a0 \u00a0 \u00a0e) kelvin \u00a0 \u00a0 \u00a0f) square meters \u00a0 \u00a0 \u00a0g) cubic meters<\/p>\r\n<p id=\"fs-idm341565728\">21. a) centi-, \u00d7 10<sup>\u22122 \u00a0 \u00a0\u00a0<\/sup>\u00a0b) deci-, \u00d7 10<sup>\u22121 \u00a0 \u00a0\u00a0<\/sup>\u00a0c) Giga-, \u00d7 10<sup>9 \u00a0 \u00a0\u00a0<\/sup>\u00a0d) kilo-, \u00d7 10<sup>3 \u00a0 \u00a0\u00a0<\/sup>\u00a0e) milli-, \u00d7 10<sup>\u22123 \u00a0 \u00a0\u00a0<\/sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0f) nano-, \u00d7 10<sup>\u22129 \u00a0 \u00a0\u00a0<\/sup>\u00a0g) pico-, \u00d7 10<sup>\u221212 \u00a0 \u00a0\u00a0<\/sup>\u00a0h) tera-, \u00d7 10<sup>12<\/sup><\/p>\r\n<p id=\"fs-idp31066016\">22. a) 8.00 kg, 5.00 L, 1.60 kg\/L \u00a0 \u00a0 \u00a0b) 2.00 kg, 5.00 L, 0.400 kg\/L \u00a0 \u00a0 \u00a0c) red &lt; green &lt; blue &lt; yellow \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0d) If the volumes are the same, then the density is directly proportional to the mass.<\/p>\r\n<p id=\"fs-idm315474368\">23. a) and b) answer is one of the following. A\/yellow: mass = 65.14 kg, volume = 3.38 L, density = 19.3 kg\/L, likely identity = gold. B\/blue: mass = 0.64 kg, volume = 1.00 L, density = 0.64 kg\/L, likely identity = apple. C\/green: mass = 4.08 kg, volume = 5.83 L, density = 0.700 kg\/L, likely identity = gasoline. D\/red: mass = 3.10 kg, volume = 3.38 L, density = 0.920 kg\/L, likely identity = ice; and E\/purple: mass = 3.53 kg, volume = 1.00 L, density = 3.53 kg\/L, likely identity = diamond. (c) B\/blue\/apple (0.64 kg\/L) &lt; C\/green\/gasoline (0.700 kg\/L) &lt; C\/green\/ice (0.920 kg\/L) &lt; D\/red\/diamond (3.53 kg\/L) &lt; A\/yellow\/gold (19.3 kg\/L)<\/p>\r\n\r\n<\/div>\r\n<div>\r\n<h2>Glossary<\/h2>\r\n<strong>Celsius (\u00b0C):<\/strong> unit of temperature; water freezes at 0 \u00b0C and boils at 100 \u00b0C on this scale\r\n\r\n<strong>cubic centimeter (cm<sup>3<\/sup> or cc):<\/strong>\u00a0volume of a cube with an edge length of exactly 1 cm\r\n\r\n<strong>cubic meter (m<sup>3<\/sup>):\u00a0<\/strong>SI unit of volume\r\n\r\n<strong>density:\u00a0<\/strong>ratio of mass to volume for a substance or object\r\n\r\n<strong>kelvin (K):\u00a0<\/strong>SI unit of temperature; 273.15 K = 0 \u00baC\r\n\r\n<strong>kilogram (kg):\u00a0<\/strong>standard SI unit of mass; 1 kg = approximately 2.2 pounds\r\n\r\n<strong>length:\u00a0<\/strong>measure of one dimension of an object\r\n\r\n<strong>liter (L):\u00a0<\/strong>(also, cubic decimeter) unit of volume; 1 L = 1,000 cm<sup>3<\/sup>\r\n\r\n<strong>meter (m):\u00a0<\/strong>standard metric and SI unit of length; 1 m = approximately 1.094 yards\r\n\r\n<strong>milliliter (mL):\u00a0<\/strong>1\/1,000 of a liter; equal to 1 cm<sup>3<\/sup>\r\n\r\n<strong>second (s):\u00a0<\/strong>SI unit of time\r\n\r\n<strong>SI units (International System of Units):\u00a0<\/strong>standards fixed by international agreement in the International System of Units (<em>Le Syst\u00e8me International d\u2019Unit\u00e9s<\/em>)\r\n\r\n<strong>unit:\u00a0<\/strong>standard of comparison for measurements\r\n\r\n<strong>volume:\u00a0<\/strong>amount of space occupied by an object\r\n\r\n<\/div>","rendered":"<div>\n<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Objectives<\/h3>\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Explain the process of measurement<\/li>\n<li>Identify the three basic parts of a quantity<\/li>\n<li>Describe the properties and units of length, mass, volume, density, temperature, and time<\/li>\n<li>Perform basic unit calculations and conversions in the metric and other unit systems<\/li>\n<\/ul>\n<\/div>\n<p>The development of modern chemistry is often attributed to 18th century Frenchman Antoine-Laurent de Lavoisier, who was able though meticulous and careful scientific measurements that during a chemical reaction mass is neither consumed or created, the principle that led to <strong>the law of conservation of mass<\/strong>, one of the important fundamental principles in your study of chemistry. It is fundamentally important to realize that a science is for the most part a quantitative endeavor. Our ability to make observations through numerical measures is one of the cornerstones of the scientific method.<\/p>\n<p id=\"fs-idm75764096\">Measurements provide the macroscopic information that is the basis of most of the hypotheses, theories, and laws that describe the behavior of matter and energy in both the macroscopic and microscopic domains of chemistry. Every measurement provides three kinds of information: a number (quantitative observation), a unit (describes how it was measured), and the degree of reliability (uncertainty of the measurement). While the number and unit are explicitly represented when a quantity is written, the uncertainty is an aspect of the measurement result that is more implicitly represented and will be discussed later.<\/p>\n<p id=\"fs-idm128012432\">The number in the measurement can be represented in different ways, including decimal form and scientific notation. For example, the maximum takeoff weight of a Boeing 777-200ER airliner is 298,000 kilograms, which can also be written as 2.98 \u00d7 10<sup>5<\/sup> kg. The mass of the average mosquito is about 0.0000025 kilograms, which can be written as 2.5 \u00d7 10<sup>\u22126<\/sup> kg.<\/p>\n<p id=\"fs-idp178656\"><strong>Units<\/strong>, such as liters, pounds, and centimeters, are standards of comparison for measurements. When we buy a 2-liter bottle of a soft drink, we expect that the volume of the drink was measured, so it is two times larger than the volume that everyone agrees to be 1 liter. The meat used to prepare a 0.25-pound hamburger is measured so it weighs one-fourth as much as 1 pound. Without units, a number can be meaningless, confusing, or possibly life threatening. Suppose a doctor prescribes phenobarbital to control a patient\u2019s seizures and states a dosage of \u201c100\u201d without specifying units. Not only will this be confusing to the medical professional giving the dose, but the consequences can be dire: 100 mg given three times per day can be effective as an anticonvulsant, but a single dose of 100 g is more than 10 times the lethal amount.<\/p>\n<p id=\"fs-idm144392592\">We usually report the results of scientific measurements in SI units, an updated version of the metric system, using the units listed in <a href=\"#fs-idm81346144\" class=\"autogenerated-content\">Table 1<\/a>. Other units can be derived from these base units. The standards for these units are fixed by international agreement, and they are called the <strong>International System of Units<\/strong> or <strong>SI Units<\/strong> (from the French, <em>Le Syst\u00e8me International d\u2019Unit\u00e9s<\/em>). SI units have been used by the United States National Institute of Standards and Technology (NIST) since 1964.<\/p>\n<table id=\"fs-idm81346144\" class=\"span-all\" summary=\"Length is measured with the meter, which is symbolized using a lowercase M. Mass is measured with the kilogram which is symbolized with a lowercase K G. Time is measured with the second, which is symbolized with a lowercase S. Temperature is measured with the kelvin which is symbolized with an uppercase K. Electric current is measured with the ampere which is symbolized with an uppercase A. The amount of a substance is measured with the mole, which is symbolized with the lowercase letters, M O L. Luminous intensity is measured with the candela, which is symbolized with the lowercase letters C D.\">\n<thead>\n<tr valign=\"top\">\n<th>Property Measured<\/th>\n<th>Name of Unit<\/th>\n<th>Symbol of Unit<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>length<\/td>\n<td>meter<\/td>\n<td>m<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>mass<\/td>\n<td>kilogram<\/td>\n<td>kg<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>time<\/td>\n<td>second<\/td>\n<td>s<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>temperature<\/td>\n<td>kelvin<\/td>\n<td>K<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>electric current<\/td>\n<td>ampere<\/td>\n<td>A<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>amount of substance<\/td>\n<td>mole<\/td>\n<td>mol<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>luminous intensity<\/td>\n<td>candela<\/td>\n<td>cd<\/td>\n<\/tr>\n<tr>\n<td colspan=\"3\"><strong>Table 1.<\/strong> Base Units of the SI System<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"eip-134\">Sometimes we use units that are fractions or multiples of a base unit. Ice cream is sold in quarts (a familiar, non-SI base unit), pints (0.5 quart), or gallons (4 quarts). We also use fractions or multiples of units in the SI system, but these fractions or multiples are always powers of 10. Fractional or multiple SI units are named using a prefix and the name of the base unit. For example, a length of 1000 meters is also called a kilometer because the prefix <em>kilo<\/em> means \u201cone thousand,\u201d which in scientific notation is 10<sup>3<\/sup> (1 kilometer = 1000 m = 10<sup>3<\/sup> m). The prefixes used and the powers to which 10 are raised are listed in <a href=\"#fs-idm81128320\" class=\"autogenerated-content\">Table 2<\/a>.<\/p>\n<div id=\"fs-idp86805728\" class=\"textbox shaded\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/CNX_Interactive_200DPI-1-2.png\" alt=\"\" width=\"122\" height=\"76\" class=\"alignleft\" \/><\/p>\n<p id=\"fs-idm169361696\">Need a refresher or more practice with scientific notation? Visit this <a href=\"http:\/\/openstaxcollege.org\/l\/16notation\">site<\/a> to go over the basics of scientific notation.<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<table id=\"fs-idm81128320\" class=\"span-all\" summary=\"The prefix femto has the symbol lowercase f and a factor of 10 to the negative fifteenth power. Therefore, 1 femtosecond, F S, is equal to 1 times 10 to the negative 15 of a meter, or 0.000000000001 of a meter. The prefix pico has the symbol lowercase P and a factor of 10 to the negative twelfth power. Therefore, 1 picosecond, P S, is equal to 1 times 10 to the negative 12 of a meter, or 0.000000000001 of a meter. The prefix nano has the symbol lowercase N and a factor of 10 to the negative ninth power. Therefore, 4 nanograms, or NG, equals 4 times ten to the negative 9, or 0.000000004 g. The prefix micro has the greek letter mu as its symbol and a factor of 10 to the negative sixth power. Therefore, 1 microliter, or mu L, is equal to one times ten to the negative 6 or 0.000001 L. The prefix milli has a lowercase M as its symbol and a factor of 10 to the negative third power. Therefore, 2 millimoles, or M mol, are equal to two times ten to the negative 3 or 0.002 mol. The prefix centi has a lowercase C as its symbol and a factor of 10 to the negative second power. Therefore, 7 centimeters, or C M, are equal to seven times ten to the negative 2 meters or 0.07 M O L. The prefix deci has a lowercase D as its symbol and a factor of 10 to the negative first power. Therefore, 1 deciliter, or lowercase D uppercase L, are equal to one times ten to the negative 1 meters or 0.1 L. The prefix kilo has a lowercase K as its symbol and a factor of 10 to the third power. Therefore, 1 kilometer, or K M, is equal to one times ten to the third meters or 1000 M. The prefix mega has an uppercase M as its symbol and a factor of 10 to the sixth power. Therefore, 3 megahertz, or M H Z, are equal to three times 10 to the sixth hertz, or 3000000 H Z. The prefix giga has an uppercase G as its symbol and a factor of 10 to the ninth power. Therefore, 8 gigayears, or G Y R, are equal to eight times 10 to the ninth years, or 800000000 G Y R. The prefix tera has an uppercase T as its symbol and a factor of 10 to the twelfth power. Therefore, 5 terawatts, or T W, are equal to five times 10 to the twelfth watts, or 5000000000000 W.\">\n<thead>\n<tr valign=\"top\">\n<th style=\"width: 45px\">Prefix<\/th>\n<th style=\"width: 56px\">Symbol<\/th>\n<th style=\"width: 49px\">Factor<\/th>\n<th style=\"width: 369px\">Example<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td style=\"width: 45px\">femto<\/td>\n<td style=\"width: 56px\">f<\/td>\n<td style=\"width: 49px\">10<sup>\u221215<\/sup><\/td>\n<td style=\"width: 369px\">1 femtosecond (fs) = 1 \u00d7 10<sup>\u221215<\/sup> s (0.000000000000001 s)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 45px\">pico<\/td>\n<td style=\"width: 56px\">p<\/td>\n<td style=\"width: 49px\">10<sup>\u221212<\/sup><\/td>\n<td style=\"width: 369px\">1 picometer (pm) = 1 \u00d7 10<sup>\u221212<\/sup> m (0.000000000001 m)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 45px\">nano<\/td>\n<td style=\"width: 56px\">n<\/td>\n<td style=\"width: 49px\">10<sup>\u22129<\/sup><\/td>\n<td style=\"width: 369px\">4 nanograms (ng) = 4 \u00d7 10<sup>\u22129<\/sup> g (0.000000004 g)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 45px\">micro<\/td>\n<td style=\"width: 56px\">\u00b5<\/td>\n<td style=\"width: 49px\">10<sup>\u22126<\/sup><\/td>\n<td style=\"width: 369px\">1 microliter (\u03bcL) = 1 \u00d7 10<sup>\u22126<\/sup> L (0.000001 L)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 45px\">milli<\/td>\n<td style=\"width: 56px\">m<\/td>\n<td style=\"width: 49px\">10<sup>\u22123<\/sup><\/td>\n<td style=\"width: 369px\">2 millimoles (mmol) = 2 \u00d7 10<sup>\u22123<\/sup> mol (0.002 mol)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 45px\">centi<\/td>\n<td style=\"width: 56px\">c<\/td>\n<td style=\"width: 49px\">10<sup>\u22122<\/sup><\/td>\n<td style=\"width: 369px\">7 centimeters (cm) = 7 \u00d7 10<sup>\u22122<\/sup> m (0.07 m)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 45px\">deci<\/td>\n<td style=\"width: 56px\">d<\/td>\n<td style=\"width: 49px\">10<sup>\u22121<\/sup><\/td>\n<td style=\"width: 369px\">1 deciliter (dL) = 1 \u00d7 10<sup>\u22121<\/sup> L (0.1 L )<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 45px\">kilo<\/td>\n<td style=\"width: 56px\">k<\/td>\n<td style=\"width: 49px\">10<sup>3<\/sup><\/td>\n<td style=\"width: 369px\">1 kilometer (km) = 1 \u00d7 10<sup>3<\/sup> m (1000 m)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 45px\">mega<\/td>\n<td style=\"width: 56px\">M<\/td>\n<td style=\"width: 49px\">10<sup>6<\/sup><\/td>\n<td style=\"width: 369px\">3 megahertz (MHz) = 3 \u00d7 10<sup>6<\/sup> Hz (3,000,000 Hz)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 45px\">giga<\/td>\n<td style=\"width: 56px\">G<\/td>\n<td style=\"width: 49px\">10<sup>9<\/sup><\/td>\n<td style=\"width: 369px\">8 gigayears (Gyr) = 8 \u00d7 10<sup>9<\/sup> yr (8,000,000,000 Gyr)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 45px\">tera<\/td>\n<td style=\"width: 56px\">T<\/td>\n<td style=\"width: 49px\">10<sup>12<\/sup><\/td>\n<td style=\"width: 369px\">5 terawatts (TW) = 5 \u00d7 10<sup>12<\/sup> W (5,000,000,000,000 W)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 519px\" colspan=\"4\"><strong>Table 2.<\/strong> Common Unit Prefixes<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<section id=\"fs-idp25374912\">\n<h2>SI Base Units<\/h2>\n<p id=\"fs-idp389936\">The initial units of the metric system, which eventually evolved into the SI system, were established in France during the French Revolution. The original standards for the meter and the kilogram were adopted there in 1799 and eventually by other countries. This section introduces four of the SI base units commonly used in chemistry. Other SI units will be introduced in subsequent chapters.<\/p>\n<section id=\"fs-idp679312\">\n<h2>Length<\/h2>\n<p id=\"fs-idm64613648\">The standard unit of <strong>length<\/strong> in both the SI and original metric systems is the <strong>meter (m)<\/strong>. A meter was originally specified as 1\/10,000,000 of the distance from the North Pole to the equator. It is now defined as the distance light in a vacuum travels in 1\/299,792,458 of a second. A meter is about 3 inches longer than a yard (<a href=\"#CNX_Chem_01_04_MYdCmIn\" class=\"autogenerated-content\">Figure 1<\/a>); one meter is about 39.37 inches or 1.094 yards. Longer distances are often reported in kilometers (1 km = 1000 m = 10<sup>3<\/sup> m), whereas shorter distances can be reported in centimeters (1 cm = 0.01 m = 10<sup>\u22122<\/sup> m) or millimeters (1 mm = 0.001 m = 10<sup>\u22123<\/sup> m).<\/p>\n<figure id=\"CNX_Chem_01_04_MYdCmIn\">\n<figure style=\"width: 1300px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/CNX_Chem_01_04_MYdCmIn-2.jpg\" alt=\"One meter is slightly larger than a yard and one centimeter is less than half the size of one inch. 1 inch is equal to 2.54 cm. 1 m is equal to 1.094 yards which is equal to 39.36 inches.\" width=\"1300\" height=\"639\" \/><figcaption class=\"wp-caption-text\"><strong>Figure 1.<\/strong> The relative lengths of 1 m, 1 yd, 1 cm, and 1 in. are shown (not actual size), as well as comparisons of 2.54 cm and 1 in., and of 1 m and 1.094 yd.<\/figcaption><\/figure>\n<\/figure>\n<\/section>\n<section id=\"fs-idm1313360\">\n<h2>Mass<\/h2>\n<p id=\"fs-idp222999216\">The standard unit of mass in the SI system is the <strong>kilogram (kg)<\/strong>. A kilogram was originally defined as the mass of a liter of water (a cube of water with an edge length of exactly 0.1 meter). It is now defined by a certain cylinder of platinum-iridium alloy, which is kept in France (<a href=\"#CNX_Chem_01_04_Kilogram\" class=\"autogenerated-content\">Figure 2<\/a>). Any object with the same mass as this cylinder is said to have a mass of 1 kilogram. One kilogram is about 2.2 pounds. The gram (g) is exactly equal to 1\/1000 of the mass of the kilogram (10<sup>\u22123<\/sup> kg).<\/p>\n<figure id=\"CNX_Chem_01_04_Kilogram\">\n<figure id=\"attachment_1282\" aria-describedby=\"caption-attachment-1282\" style=\"width: 200px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/CNX_Chem_01_04_Kilogram-2-e1528931146214.jpg\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/CNX_Chem_01_04_Kilogram-2-e1528931146214.jpg\" alt=\"\" width=\"200\" height=\"283\" class=\"wp-image-1282 size-full\" \/><\/a><figcaption id=\"caption-attachment-1282\" class=\"wp-caption-text\"><strong>Figure 2.<\/strong> This replica prototype kilogram is housed at the National Institute of Standards and Technology (NIST) in Maryland. (credit: National Institutes of Standards and Technology)<\/figcaption><\/figure>\n<\/figure>\n<\/section>\n<section id=\"fs-idm1531808\">\n<h2>Temperature<\/h2>\n<p id=\"fs-idp3379184\">Temperature is an intensive property. The SI unit of temperature is the <strong>kelvin (K)<\/strong>. The IUPAC convention is to use kelvin (all lowercase) for the word, K (uppercase) for the unit symbol, and neither the word \u201cdegree\u201d nor the degree symbol (\u00b0). The degree <strong>Celsius (\u00b0C)<\/strong> is also allowed in the SI system, with both the word \u201cdegree\u201d and the degree symbol used for Celsius measurements. Celsius degrees are the same magnitude as those of kelvin, but the two scales place their zeros in different places. Water freezes at 273.15 K (0 \u00b0C) and boils at 373.15 K (100 \u00b0C) by definition, and normal human body temperature is approximately 310 K (37 \u00b0C). The conversion between these two units and the Fahrenheit scale will be discussed later in this chapter.<\/p>\n<\/section>\n<section id=\"fs-idm101578432\">\n<h2>Time<\/h2>\n<p id=\"fs-idm101738864\">The SI base unit of time is the <strong>second (s)<\/strong>. Small and large time intervals can be expressed with the appropriate prefixes; for example, 3 microseconds = 0.000003 s = 3 \u00d7 10<sup>\u22126<\/sup> and 5 megaseconds = 5,000,000 s = 5 \u00d7 10<sup>6<\/sup> s. Alternatively, hours, days, and years can be used.<\/p>\n<\/section>\n<\/section>\n<section id=\"fs-idm23668768\">\n<h2>Derived SI Units<\/h2>\n<p id=\"fs-idm10854912\">We can derive many units from the seven SI base units. For example, we can use the base unit of length to define a unit of volume, and the base units of mass and length to define a unit of density.<\/p>\n<section id=\"fs-idm16046736\">\n<h2>Volume<\/h2>\n<p id=\"fs-idm77137776\"><strong>Volume<\/strong> is the measure of the amount of space occupied by an object. The standard SI unit of volume is defined by the base unit of length (<a href=\"#CNX_Chem_01_04_Volume\" class=\"autogenerated-content\">Figure 3<\/a>). The standard volume is a <strong>cubic meter (m<sup>3<\/sup>)<\/strong>, a cube with an edge length of exactly one meter. To dispense a cubic meter of water, we could build a cubic box with edge lengths of exactly one meter. This box would hold a cubic meter of water or any other substance.<\/p>\n<p id=\"fs-idm81813264\">A more commonly used unit of volume is derived from the decimeter (0.1 m, or 10 cm). A cube with edge lengths of exactly one decimeter contains a volume of one cubic decimeter (dm<sup>3<\/sup>). A <strong>liter (L) <\/strong> is the more common name for the cubic decimeter. One liter is about 1.06 quarts.<\/p>\n<p id=\"fs-idm163691744\">A <strong>cubic centimeter (cm<sup>3<\/sup>)<\/strong> is the volume of a cube with an edge length of exactly one centimeter. The abbreviation <strong>cc<\/strong> (for <strong>c<\/strong>ubic <strong>c<\/strong>entimeter) is often used by health professionals. A cubic centimeter is also called a <strong>milliliter (mL)<\/strong> and is 1\/1000 of a liter.<\/p>\n<figure id=\"CNX_Chem_01_04_Volume\">\n<figure style=\"width: 1200px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/CNX_Chem_01_04_Volume-2.jpg\" alt=\"Figure A shows a large cube, which has a volume of 1 meter cubed. This larger cube is made up of many smaller cubes in a 10 by 10 pattern. Each of these smaller cubes has a volume of 1 decimeter cubed, or one liter. Each of these smaller cubes is, in turn, made up of many tiny cubes. Each of these tiny cubes has a volume of 1 centimeter cubed, or one milliliter. A one cubic centimeter cube is about the same width as a dime, which has a width of 1.8 centimeter.\" width=\"1200\" height=\"675\" \/><figcaption class=\"wp-caption-text\"><strong>Figure 3<\/strong> (a) The relative volumes are shown for cubes of 1 m<sup>3<\/sup>, 1 dm<sup>3<\/sup> (1 L), and 1 cm<sup>3<\/sup> (1 mL) (not to scale). (b) The diameter of a dime is compared relative to the edge length of a 1-cm<sup>3<\/sup> (1-mL) cube.<\/figcaption><\/figure>\n<\/figure>\n<\/section>\n<section id=\"fs-idm18447104\">\n<h2>Density<\/h2>\n<p id=\"fs-idp205372288\">We use the mass and volume of a substance to determine its density. Thus, the units of density are defined by the base units of mass and length.<\/p>\n<p id=\"fs-idm74744496\">The <strong>density<\/strong> of a substance is the ratio of the mass of a sample of the substance to its volume. The SI unit for density is the kilogram per cubic meter (kg\/m<sup>3<\/sup>). For many situations, however, this as an inconvenient unit, and we often use grams per cubic centimeter (g\/cm<sup>3<\/sup>) for the densities of solids and liquids, and grams per liter (g\/L) for gases. Although there are exceptions, most liquids and solids have densities that range from about 0.7 g\/cm<sup>3<\/sup> (the density of gasoline) to 19 g\/cm<sup>3<\/sup> (the density of gold). The density of air is about 1.2 g\/L. <a href=\"#fs-idm45639696\" class=\"autogenerated-content\">Table 3<\/a> shows the densities of some common substances.<\/p>\n<table id=\"fs-idm45639696\" class=\"span-all\" summary=\"This table reports the density of solids, liquids, and gases in grams per centimeters cubed. The values for solids are ice 0.92, oak wood 0.60 to 0.90, iron 7.9, copper 9.0, lead 11.3, silver 10.5, and gold 19.3. The values for liquids are water 1.0, ethanol 0.79, acetone 0.79, glycerin 1.26, olive oil 0.92, gasoline 0.70 to 0.77, and Mercury 13.6. The values for gases, which were measured when the gas was at 25 degrees Celsius and 1 atmosphere, are dry air 1.20, oxygen 1.31, nitrogen 1.14, carbon dioxide 1.80, helium 0.16, neon 0.83, and radon 9.1.\">\n<thead>\n<tr valign=\"top\">\n<th>Solids<\/th>\n<th>Liquids<\/th>\n<th>Gases (at 25 \u00b0C and 1 atm)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>ice (at 0 \u00b0C) 0.92 g\/cm<sup>3<\/sup><\/td>\n<td>water 1.0 g\/cm<sup>3<\/sup><\/td>\n<td>dry air 1.20 g\/L<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>oak (wood) 0.60\u20130.90 g\/cm<sup>3<\/sup><\/td>\n<td>ethanol 0.79 g\/cm<sup>3<\/sup><\/td>\n<td>oxygen 1.31 g\/L<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>iron 7.9 g\/cm<sup>3<\/sup><\/td>\n<td>acetone 0.79 g\/cm<sup>3<\/sup><\/td>\n<td>nitrogen 1.14 g\/L<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>copper 9.0 g\/cm<sup>3<\/sup><\/td>\n<td>glycerin 1.26 g\/cm<sup>3<\/sup><\/td>\n<td>carbon dioxide 1.80 g\/L<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>lead 11.3 g\/cm<sup>3<\/sup><\/td>\n<td>olive oil 0.92 g\/cm<sup>3<\/sup><\/td>\n<td>helium 0.16 g\/L<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>silver 10.5 g\/cm<sup>3<\/sup><\/td>\n<td>gasoline 0.70\u20130.77 g\/cm<sup>3<\/sup><\/td>\n<td>neon 0.83 g\/L<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>gold 19.3 g\/cm<sup>3<\/sup><\/td>\n<td>mercury 13.6 g\/cm<sup>3<\/sup><\/td>\n<td>radon 9.1 g\/L<\/td>\n<\/tr>\n<tr>\n<td colspan=\"3\"><strong>Table 3.<\/strong> Densities of Common Substances<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-idm81523280\">While there are many ways to determine the density of an object, perhaps the most straightforward method involves separately finding the mass and volume of the object, and then dividing the mass of the sample by its volume. In the following example, the mass is found directly by weighing, but the volume is found indirectly through length measurements.<\/p>\n<div class=\"equation\" id=\"fs-idm166517584\" style=\"text-align: center\">[latex]\\text{density} = \\frac{\\text{mass}}{\\text{volume}}[\/latex]<\/div>\n<\/section>\n<div class=\"textbox shaded\" id=\"Example_01_04_01\">\n<h3>Example 1<\/h3>\n<p>Gold\u2014in bricks, bars, and coins\u2014has been a form of currency for centuries. In order to swindle people into paying for a brick of gold without actually investing in a brick of gold, people have considered filling the centers of hollow gold bricks with lead to fool buyers into thinking that the entire brick is gold. It does not work: Lead is a dense substance, but its density is not as great as that of gold, 19.3 g\/cm<sup>3<\/sup>. What is the density of lead if a cube of lead has an edge length of 2.00 cm and a mass of 90.7 g?<\/p>\n<p>&nbsp;<\/p>\n<p id=\"fs-idp40298832\"><strong>Solution<\/strong><br \/>\nThe density of a substance can be calculated by dividing its mass by its volume. The volume of a cube is calculated by cubing the edge length.<\/p>\n<p style=\"text-align: center\">[latex]\\text{volume of lead cube}=2.00\\text{cm}\\times2.00\\text{cm}\\times2.00\\text{cm}=9.00\\text{cm}^3[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]\\text{density}=\\frac{\\text{mass}}{\\text{volume}}=\\frac{90.7\\text{g}}{8.00\\text{cm}^3}=\\frac{11.3\\text{g}}{1.00\\text{cm}^3}=11.3\\;\\text{g}\/\\text{cm}^3[\/latex]<\/p>\n<div class=\"example\">\n<div class=\"equation\" id=\"fs-idm163080256\" style=\"text-align: center\"><\/div>\n<p id=\"fs-idp264752\">(We will discuss the reason for rounding to the first decimal place in the next section.)<\/p>\n<p>&nbsp;<\/p>\n<p id=\"fs-idp2742064\"><strong><em>Test Yourself<\/em><\/strong><br \/>\na) To three decimal places, what is the volume of a cube (cm<sup>3<\/sup>) with an edge length of 0.843 cm?<\/p>\n<p id=\"fs-idp116749488\">b) If the cube in part a) is copper and has a mass of 5.34 g, what is the density of copper to two decimal places?<\/p>\n<p>&nbsp;<\/p>\n<p><strong><em>Answers<\/em><\/strong><\/p>\n<p>a) 0.599 cm<sup>3<\/sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 b) 8.91 g\/cm<sup>3<\/sup><\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idm83823632\" class=\"textbox shaded\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/CNX_Interactive_200DPI-1-2.png\" alt=\"\" width=\"129\" height=\"80\" class=\"alignleft\" \/><\/p>\n<p>&nbsp;<\/p>\n<p id=\"fs-idm108028240\">To learn more about the relationship between mass, volume, and density, use this <a href=\"http:\/\/openstaxcollege.org\/l\/16phetmasvolden\">interactive simulator<\/a> to explore the density of different materials, like wood, ice, brick, and aluminum.<\/p>\n<\/div>\n<div class=\"textbox shaded\" id=\"Example_01_04_02\">\n<h3>Example 2<\/h3>\n<p id=\"fs-idm108240880\">This <a href=\"http:\/\/openstaxcollege.org\/l\/16phetmasvolden\">PhET simulation<\/a> illustrates another way to determine density, using displacement of water. Determine the density of the red and yellow blocks.<\/p>\n<p>&nbsp;<\/p>\n<p id=\"fs-idp206606992\"><strong>Solution<\/strong><br \/>\nWhen you open the density simulation and select Same Mass, you can choose from several 5.00-kg colored blocks that you can drop into a tank containing 100.00 L water. The yellow block floats (it is less dense than water), and the water level rises to 105.00 L. While floating, the yellow block displaces 5.00 L water, an amount equal to the weight of the block. The red block sinks (it is more dense than water, which has density = 1.00 kg\/L), and the water level rises to 101.25 L.<\/p>\n<p id=\"fs-idm85356448\">The red block therefore displaces 1.25 L water, an amount equal to the volume of the block. The density of the red block is:<\/p>\n<div class=\"equation\" id=\"fs-idm94054304\" style=\"text-align: center\">[latex]\\text{density}=\\frac{\\text{mass}}{\\text{volume}}=\\frac{5.00\\;\\text{kg}}{1.25\\;\\text{L}}=4.00 \\text{kg\/L}[\/latex]<\/div>\n<p id=\"fs-idm92012848\">Note that since the yellow block is not completely submerged, you cannot determine its density from this information. But if you hold the yellow block on the bottom of the tank, the water level rises to 110.00 L, which means that it now displaces 10.00 L water, and its density can be found:<\/p>\n<div class=\"equation\" id=\"fs-idm174274016\">\n<p style=\"text-align: center\">[latex]\\text{density}=\\frac{\\text{mass}}{\\text{volume}}=\\frac{\\text{5.00 kg}}{\\text{10.00 L}}=0.500 \\text{kg\/L}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p id=\"fs-idp10631184\" style=\"text-align: left\"><strong><em>Test Yourself<\/em><\/strong><br \/>\nRemove all of the blocks from the water and add the green block to the tank of water, placing it approximately in the middle of the tank. Determine the density of the green block.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: left\"><strong><em>Answer<\/em><\/strong><\/p>\n<p style=\"text-align: left\">2.00 kg\/L<\/p>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n<div class=\"textbox shaded\">\n<div class=\"callout block\" id=\"ball-ch03_n01\">\n<h3><strong>The Angstrom Unit<\/strong><\/h3>\n<p class=\"title\">Although not an SI unit, the angstrom (\u00c5) is a useful unit of length. It is one ten-billionth of a meter, or 10<sup class=\"superscript\">\u221210<\/sup>\u00a0m. Why is it a useful unit? The ultimate particles that compose all matter are about 10<sup class=\"superscript\">\u221210<\/sup> m in size, or about 1 \u00c5. This makes the angstrom a natural\u2014though not approved\u2014unit for describing these particles.<\/p>\n<p id=\"ball-ch03_p02\" class=\"para\">The angstrom unit is named after Anders Jonas \u00c5ngstr\u00f6m, a nineteenth-century Swedish physicist. \u00c5ngstr\u00f6m\u2019s research dealt with light being emitted by glowing objects, including the sun. \u00c5ngstr\u00f6m studied the brightness of the different colors of light that the sun emitted and was able to deduce that the sun is composed of the same kinds of matter that are present on the earth. By extension, we now know that all matter throughout the universe is similar to the matter that exists on our own planet.<\/p>\n<p class=\"para\"><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/09\/The-Sun.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/The-Sun-1.png\" alt=\"The Sun\" width=\"400\" height=\"229\" class=\"wp-image-4624 aligncenter\" \/><\/a><\/p>\n<div class=\"informalfigure large\" id=\"ball-ch03_f01\">\n<p class=\"para\">Anders Jonas \u00c5ngstrom, a Swedish physicist, studied the light coming from the sun. His contributions to science were sufficient to have a tiny unit of length named after him, the angstrom, which is one ten-billionth of a meter.<\/p>\n<div class=\"copyright\">\n<p class=\"para\">Source: Photo of the sun courtesy of NASA\u2019s Solar Dynamics Observatory, <a class=\"link\" href=\"http:\/\/commons.wikimedia.org\/wiki\/File:The_Sun_by_the_Atmospheric_Imaging_Assembly_of_NASA%27s_Solar_Dynamics_Observatory_-_20100801.jpg\" target=\"_blank\" rel=\"noopener\">http:\/\/commons.wikimedia.org\/wiki\/File:The_Sun_by_the_Atmospheric_Imaging_Assembly_of_NASA%27s_Solar_Dynamics_Observatory_-_20100801.jpg<\/a>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div>\n<section id=\"fs-idm333536464\" class=\"summary\">\n<h2>Key Concepts and Summary<\/h2>\n<p id=\"fs-idm330017088\">Measurements provide quantitative information that is critical in studying and practicing chemistry. Each measurement has an amount, a unit for comparison, and an uncertainty. Measurements can be represented in either decimal or scientific notation. Scientists primarily use the SI (International System) or metric systems. We use base SI units such as meters, seconds, and kilograms, as well as derived units, such as liters (for volume) and g\/cm<sup>3<\/sup> (for density). In many cases, we find it convenient to use unit prefixes that yield fractional and multiple units, such as microseconds (10<sup>\u22126<\/sup> seconds) and megahertz (10<sup>6<\/sup> hertz), respectively.<\/p>\n<\/section>\n<section id=\"fs-idm313032912\" class=\"key-equations\">\n<h2>Key Equations<\/h2>\n<ul id=\"fs-idm76167888\">\n<li>[latex]\\text{density}=\\frac{\\text{mass}}{\\text{volume}}[\/latex]<\/li>\n<\/ul>\n<div class=\"textbox examples\">\n<h3 itemprop=\"educationalUse\">Activity<\/h3>\n<p>Make yourself a stack of small sized Qcards to help you learn your common unit prefixes, which is important because you will use later as conversion factors for unit conversions. \u00a0On one side have the common unit prefix associated with a base unit (e.g. 1 kg) and on the other side have its equivalence in terms of the base unit (e.g. 10<sup>3<\/sup> g). \u00a0Make a complete set of using all the common unit prefixes from Table 2 and pick and choose different base units from Table 1. \u00a0Then use these Qcards to quiz yourself.<\/p>\n<\/div>\n<\/section>\n<\/div>\n<div class=\"bcc-box bcc-info\">\n<h3>Exercises<\/h3>\n<div class=\"question\">\n<p id=\"ball-ch02_s02_qs01_p1\" class=\"para\">1. \u00a0Identify the unit in each quantity.<\/p>\n<\/div>\n<p>a) \u00a02 boxes of crayons \u00a0 \u00a0\u00a0b) \u00a03.5 grams of gold<\/p>\n<div class=\"question\">\n<p id=\"ball-ch02_s02_qs01_p2\" class=\"para\">2. \u00a0Identify the unit in each quantity.<\/p>\n<p>a) \u00a032 oz of cheddar cheese \u00a0 \u00a0\u00a0b) \u00a00.045 cm<sup class=\"superscript\">3<\/sup> of water<span style=\"font-size: 1em\">\u00a0<\/span><\/p>\n<\/div>\n<div class=\"question\">\n<p id=\"ball-ch02_s02_qs01_p3\" class=\"para\">3. \u00a0Identify the unit in each quantity.<\/p>\n<p>a) \u00a09.58 s (the current world record in the 100 m dash)<\/p>\n<p>b) \u00a06.14 m (the current world record in the pole vault)<\/p>\n<\/div>\n<div class=\"question\">\n<p id=\"ball-ch02_s02_qs01_p4\" class=\"para\">4. \u00a0Identify the unit in each quantity.<\/p>\n<p>a) \u00a02 dozen eggs<\/p>\n<p>b) \u00a02.4 km\/s (the escape velocity of the moon, which is the velocity you need at the surface to escape the moon\u2019s gravity)<\/p>\n<\/div>\n<div class=\"question\">\n<p id=\"ball-ch02_s02_qs01_p5\" class=\"para\">5. \u00a0Indicate what multiplier each prefix represents.<\/p>\n<p>a) \u00a0k \u00a0 \u00a0\u00a0b) \u00a0m \u00a0 \u00a0\u00a0c) \u00a0M<\/p>\n<\/div>\n<div class=\"question\">\n<p id=\"ball-ch02_s02_qs01_p6\" class=\"para\">6. \u00a0Indicate what multiplier each prefix represents.<\/p>\n<p>a) \u00a0c \u00a0 \u00a0\u00a0b) \u00a0G \u00a0 \u00a0\u00a0c) \u00a0\u03bc<\/p>\n<\/div>\n<p><span style=\"font-size: 1em\">7. \u00a0Give the prefix that represents each multiplier.<\/span><\/p>\n<div class=\"question\">\n<p>a) \u00a01\/1,000th \u00d7 \u00a0 \u00a0\u00a0b) \u00a01,000 \u00d7 \u00a0 \u00a0 \u00a0c) \u00a01,000,000,000 \u00d7<\/p>\n<\/div>\n<div class=\"question\">\n<p id=\"ball-ch02_s02_qs01_p8\" class=\"para\">8. \u00a0Give the prefix that represents each multiplier.<\/p>\n<p>a) \u00a01\/1,000,000,000th \u00d7 \u00a0 \u00a0\u00a0b) \u00a01\/100th \u00d7 \u00a0 \u00a0\u00a0c) \u00a01,000,000 \u00d7<\/p>\n<p>&nbsp;<\/p>\n<p>9. Complete the following table with the missing information.<\/p>\n<\/div>\n<div class=\"question\">\n<div class=\"informaltable\">\n<table style=\"border-color: #000000;border-spacing: 0px\" cellpadding=\"0\">\n<thead>\n<tr>\n<th>Unit<\/th>\n<th align=\"center\">Abbreviation<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>kilosecond<\/td>\n<td align=\"center\"><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td align=\"center\">mL<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td align=\"center\">Mg<\/td>\n<\/tr>\n<tr>\n<td>centimeter<\/td>\n<td align=\"center\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"question\">\n<p id=\"ball-ch02_s02_qs01_p10\" class=\"para\">10.Complete the following table with the missing information.<\/p>\n<div class=\"informaltable\">\n<table style=\"border-color: #000000;border-spacing: 0px\" cellpadding=\"0\">\n<thead>\n<tr>\n<th>Unit<\/th>\n<th align=\"center\">Abbreviation<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>kilometer per second<\/td>\n<td align=\"center\"><\/td>\n<\/tr>\n<tr>\n<td>second<\/td>\n<td align=\"center\"><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td align=\"center\">cm<sup class=\"superscript\">3<\/sup><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td align=\"center\">\u03bcL<\/td>\n<\/tr>\n<tr>\n<td>nanosecond<\/td>\n<td align=\"center\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>11. \u00a0Express each quantity in a more appropriate unit. There may be more than one acceptable answer.<\/p>\n<\/div>\n<\/div>\n<p>a) \u00a03.44 \u00d7 10<sup class=\"superscript\">\u22126<\/sup> s \u00a0 \u00a0\u00a0b) \u00a03,500 L \u00a0 \u00a0\u00a0c) \u00a00.045 m<\/p>\n<p><span style=\"font-size: 1em\">12. \u00a0Express each quantity in a more appropriate unit. There may be more than one acceptable answer.<\/span><\/p>\n<div class=\"question\">\n<p>a) \u00a00.000066 m\/s (Hint: you need consider only the unit in the numerator.)<\/p>\n<p>b) \u00a04.66 \u00d7 10<sup class=\"superscript\">6<\/sup> s<\/p>\n<p>c) \u00a07,654 L<\/p>\n<\/div>\n<p><span style=\"font-size: 1em\">13. \u00a0Express each quantity in a more appropriate unit. There may be more than one acceptable answer.<\/span><\/p>\n<div class=\"question\">\n<p>a) \u00a043,600 mL \u00a0 \u00a0\u00a0b) \u00a00.0000044 m \u00a0 \u00a0\u00a0c) \u00a01,438 ms<\/p>\n<\/div>\n<p><span style=\"font-size: 1em\">14. \u00a0Express each quantity in a more appropriate unit. There may be more than one acceptable answer.<\/span><\/p>\n<div class=\"question\">\n<p>a) \u00a00.000000345 m<sup class=\"superscript\">3 \u00a0 \u00a0\u00a0<\/sup>b) \u00a047,000,000 mm<sup class=\"superscript\">3 \u00a0 \u00a0\u00a0<\/sup>c) \u00a00.00665 L<\/p>\n<\/div>\n<p><span style=\"font-size: 1em\">15. \u00a0Multiplicative prefixes are used for other units as well, such as computer memory. The basic unit of computer memory is the byte (b). What is the unit for one million bytes?<\/span><\/p>\n<p><span style=\"font-size: 1em\">16. \u00a0You may have heard the terms <\/span><em class=\"emphasis\" style=\"font-size: 1em\">microscale<\/em><span style=\"font-size: 1em\"> or <\/span><em class=\"emphasis\" style=\"font-size: 1em\">nanoscale<\/em><span style=\"font-size: 1em\"> to represent the sizes of small objects. What units of length do you think are useful at these scales? What fractions of the fundamental unit of length are these units?<\/span><\/p>\n<p><span style=\"font-size: 1em\">17. \u00a0Acceleration is defined as a change in velocity per time. Propose a unit for acceleration in terms of the fundamental SI units.<\/span><\/p>\n<p><span style=\"font-size: 1em\">18. \u00a0Density is defined as the mass of an object divided by its volume. Propose a unit of density in terms of the fundamental SI units.<\/span><\/p>\n<div class=\"question\">\n<p class=\"para\"><span style=\"font-size: 1em\">19. \u00a0Is a meter about an inch, a foot, a yard, or a mile?<\/span><\/p>\n<p class=\"para\"><span style=\"font-size: 1em\">20. \u00a0Indicate the SI base units or derived units that are appropriate for the following measurements:<\/span><\/p>\n<\/div>\n<p id=\"fs-idm270779504\">a) the mass of the moon<\/p>\n<p id=\"fs-idm7152592\">b) the distance from Dallas to Oklahoma City<\/p>\n<p id=\"fs-idm241075344\">c) the speed of sound<\/p>\n<p id=\"fs-idm11255792\">d) the density of air<\/p>\n<p id=\"fs-idm386910128\">e) the temperature at which alcohol boils<\/p>\n<p id=\"fs-idm312450912\">f) the area of the state of Delaware<\/p>\n<p id=\"fs-idm332809616\">g) the volume of a flu shot or a measles vaccination<\/p>\n<p>21. \u00a0Give the name of the prefix and the quantity indicated by the following symbols that are used with SI base units.<\/p>\n<p id=\"fs-idm184430352\">a) c \u00a0 \u00a0\u00a0b) d \u00a0 \u00a0\u00a0c) G \u00a0 \u00a0\u00a0d) k \u00a0 \u00a0\u00a0e) m \u00a0 \u00a0\u00a0f) n \u00a0 \u00a0 \u00a0g) p \u00a0 \u00a0\u00a0h) T<\/p>\n<p>22. \u00a0Visit this <a href=\"http:\/\/openstaxcollege.org\/l\/16phetmasvolden\">PhET density simulation<\/a> and select the Same Volume Blocks.<\/p>\n<p id=\"fs-idm148389344\">a) What are the mass, volume, and density of the yellow block?<\/p>\n<p id=\"fs-idm329801072\">b) What are the mass, volume and density of the red block?<\/p>\n<p id=\"fs-idm344699344\">c) List the block colors in order from smallest to largest mass.<\/p>\n<p id=\"fs-idm338418880\">d) List the block colors in order from lowest to highest density.<\/p>\n<p id=\"fs-idm310048112\">e) How are mass and density related for blocks of the same volume?<\/p>\n<p>23. \u00a0Visit this <a href=\"http:\/\/openstaxcollege.org\/l\/16phetmasvolden\">PhET density simulation<\/a> and select Mystery Blocks.<\/p>\n<p id=\"fs-idm153136896\">a) Pick one of the Mystery Blocks and determine its mass, volume, density, and its likely identity.<\/p>\n<p id=\"fs-idm127620640\">b) Pick a different Mystery Block and determine its mass, volume, density, and its likely identity.<\/p>\n<p id=\"fs-idm178736144\">c) Order the Mystery Blocks from least dense to most dense. Explain.<\/p>\n<p>&nbsp;<\/p>\n<p><b>Answers<\/b><\/p>\n<p>1.\u00a0a) \u00a0boxes of crayons \u00a0 \u00a0\u00a0b) \u00a0grams of gold<\/p>\n<p id=\"ball-ch02_s02_qs01_p2\" class=\"para\">2. \u00a0a) \u00a0oz of cheddar cheese \u00a0 \u00a0\u00a0b) cm<sup class=\"superscript\">3<\/sup> of water<\/p>\n<p>3. \u00a0a) \u00a0seconds \u00a0 \u00a0\u00a0b) \u00a0meters<\/p>\n<p id=\"ball-ch02_s02_qs01_p4\" class=\"para\">4. \u00a0a) \u00a0dozen of eggs \u00a0 \u00a0\u00a0b) \u00a0km\/s<\/p>\n<p>5. \u00a0a) \u00a01,000 \u00d7 \u00a0 \u00a0 b) \u00a01\/1,000 \u00d7 \u00a0 \u00a0\u00a0c) \u00a01,000,000 \u00d7<\/p>\n<div class=\"question\">\n<p id=\"ball-ch02_s02_qs01_p6\" class=\"para\">6. \u00a0a) \u00a01\/100 x \u00a0 \u00a0 b) 1,000,000,000 x \u00a0 \u00a0 c) 1\/1,000,000 x<\/p>\n<\/div>\n<p>7. \u00a0a) \u00a0milli- \u00a0 \u00a0\u00a0b) \u00a0kilo- \u00a0 \u00a0\u00a0c) \u00a0giga-<\/p>\n<p id=\"ball-ch02_s02_qs01_p8\" class=\"para\">8. \u00a0a) \u00a0nano- \u00a0 \u00a0\u00a0b) \u00a0centi- \u00a0 \u00a0\u00a0c) \u00a0mega-<\/p>\n<p>9.<\/p>\n<div class=\"informaltable\">\n<table style=\"border-color: #000000;border-spacing: 0px\" cellpadding=\"0\">\n<thead>\n<tr>\n<th>Unit<\/th>\n<th align=\"center\">Abbreviation<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>kilosecond<\/td>\n<td align=\"center\">ks<\/td>\n<\/tr>\n<tr>\n<td>milliliter<\/td>\n<td align=\"center\">mL<\/td>\n<\/tr>\n<tr>\n<td>megagram<\/td>\n<td align=\"center\">Mg<\/td>\n<\/tr>\n<tr>\n<td>centimeter<\/td>\n<td align=\"center\">cm<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p id=\"ball-ch02_s02_qs01_p10\" class=\"para\">10.<\/p>\n<div class=\"informaltable\">\n<table style=\"border-color: #000000;border-spacing: 0px\" cellpadding=\"0\">\n<thead>\n<tr>\n<th>Unit<\/th>\n<th align=\"center\">Abbreviation<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>kilometer per second<\/td>\n<td align=\"center\">\u00a0km\/s<\/td>\n<\/tr>\n<tr>\n<td>second<\/td>\n<td align=\"center\">s<\/td>\n<\/tr>\n<tr>\n<td>\u00a0cubic centimeter<\/td>\n<td align=\"center\">cm<sup class=\"superscript\">3<\/sup><\/td>\n<\/tr>\n<tr>\n<td>\u00a0microliter<\/td>\n<td align=\"center\">\u03bcL<\/td>\n<\/tr>\n<tr>\n<td>nanosecond<\/td>\n<td align=\"center\">ns<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>11. \u00a0a) \u00a03.44 \u03bcs \u00a0 \u00a0\u00a0b) \u00a03.5 kL \u00a0 \u00a0\u00a0c) \u00a04.5 cm<\/p>\n<p>12. \u00a0a) 66 \u00b5m\/s \u00a0 \u00a0 b) 4.66 Ms \u00a0 \u00a0 c) 7.654 kL<\/p>\n<p>13. \u00a0a) \u00a043.6 L \u00a0 \u00a0\u00a0b) \u00a04.4 \u00b5m \u00a0 \u00a0\u00a0c) \u00a01.438 s<\/p>\n<p>14. \u00a0a) 345 mm<sup class=\"superscript\">3<\/sup> \u00a0 \u00a0 b) 47 dm<sup class=\"superscript\">3<\/sup> \u00a0 \u00a0 c) 6.65 mL<\/p>\n<p>15. megabytes (Mb)<\/p>\n<p>16. \u00a0<i>microscale =\u00a0\u00b5<\/i>m, 1\/1,000,000 \u00a0 \u00a0 \u00a0\u00a0<em>nanoscale =\u00a0<\/em>nm, 1\/1,000,000,000<\/p>\n<p>17. meters\/second<sup class=\"superscript\">2<\/sup><\/p>\n<p>18. kg\/m<sup class=\"superscript\">3<\/sup><\/p>\n<p id=\"fs-idm339638512\">19. about a yard<\/p>\n<p id=\"fs-idm123011200\">20. a) kilograms \u00a0 \u00a0 \u00a0b) meters \u00a0 \u00a0 \u00a0c) kilometers\/second \u00a0 \u00a0 \u00a0d) kilograms\/cubic meter \u00a0 \u00a0 \u00a0e) kelvin \u00a0 \u00a0 \u00a0f) square meters \u00a0 \u00a0 \u00a0g) cubic meters<\/p>\n<p id=\"fs-idm341565728\">21. a) centi-, \u00d7 10<sup>\u22122 \u00a0 \u00a0\u00a0<\/sup>\u00a0b) deci-, \u00d7 10<sup>\u22121 \u00a0 \u00a0\u00a0<\/sup>\u00a0c) Giga-, \u00d7 10<sup>9 \u00a0 \u00a0\u00a0<\/sup>\u00a0d) kilo-, \u00d7 10<sup>3 \u00a0 \u00a0\u00a0<\/sup>\u00a0e) milli-, \u00d7 10<sup>\u22123 \u00a0 \u00a0\u00a0<\/sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0f) nano-, \u00d7 10<sup>\u22129 \u00a0 \u00a0\u00a0<\/sup>\u00a0g) pico-, \u00d7 10<sup>\u221212 \u00a0 \u00a0\u00a0<\/sup>\u00a0h) tera-, \u00d7 10<sup>12<\/sup><\/p>\n<p id=\"fs-idp31066016\">22. a) 8.00 kg, 5.00 L, 1.60 kg\/L \u00a0 \u00a0 \u00a0b) 2.00 kg, 5.00 L, 0.400 kg\/L \u00a0 \u00a0 \u00a0c) red &lt; green &lt; blue &lt; yellow \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0d) If the volumes are the same, then the density is directly proportional to the mass.<\/p>\n<p id=\"fs-idm315474368\">23. a) and b) answer is one of the following. A\/yellow: mass = 65.14 kg, volume = 3.38 L, density = 19.3 kg\/L, likely identity = gold. B\/blue: mass = 0.64 kg, volume = 1.00 L, density = 0.64 kg\/L, likely identity = apple. C\/green: mass = 4.08 kg, volume = 5.83 L, density = 0.700 kg\/L, likely identity = gasoline. D\/red: mass = 3.10 kg, volume = 3.38 L, density = 0.920 kg\/L, likely identity = ice; and E\/purple: mass = 3.53 kg, volume = 1.00 L, density = 3.53 kg\/L, likely identity = diamond. (c) B\/blue\/apple (0.64 kg\/L) &lt; C\/green\/gasoline (0.700 kg\/L) &lt; C\/green\/ice (0.920 kg\/L) &lt; D\/red\/diamond (3.53 kg\/L) &lt; A\/yellow\/gold (19.3 kg\/L)<\/p>\n<\/div>\n<div>\n<h2>Glossary<\/h2>\n<p><strong>Celsius (\u00b0C):<\/strong> unit of temperature; water freezes at 0 \u00b0C and boils at 100 \u00b0C on this scale<\/p>\n<p><strong>cubic centimeter (cm<sup>3<\/sup> or cc):<\/strong>\u00a0volume of a cube with an edge length of exactly 1 cm<\/p>\n<p><strong>cubic meter (m<sup>3<\/sup>):\u00a0<\/strong>SI unit of volume<\/p>\n<p><strong>density:\u00a0<\/strong>ratio of mass to volume for a substance or object<\/p>\n<p><strong>kelvin (K):\u00a0<\/strong>SI unit of temperature; 273.15 K = 0 \u00baC<\/p>\n<p><strong>kilogram (kg):\u00a0<\/strong>standard SI unit of mass; 1 kg = approximately 2.2 pounds<\/p>\n<p><strong>length:\u00a0<\/strong>measure of one dimension of an object<\/p>\n<p><strong>liter (L):\u00a0<\/strong>(also, cubic decimeter) unit of volume; 1 L = 1,000 cm<sup>3<\/sup><\/p>\n<p><strong>meter (m):\u00a0<\/strong>standard metric and SI unit of length; 1 m = approximately 1.094 yards<\/p>\n<p><strong>milliliter (mL):\u00a0<\/strong>1\/1,000 of a liter; equal to 1 cm<sup>3<\/sup><\/p>\n<p><strong>second (s):\u00a0<\/strong>SI unit of time<\/p>\n<p><strong>SI units (International System of Units):\u00a0<\/strong>standards fixed by international agreement in the International System of Units (<em>Le Syst\u00e8me International d\u2019Unit\u00e9s<\/em>)<\/p>\n<p><strong>unit:\u00a0<\/strong>standard of comparison for measurements<\/p>\n<p><strong>volume:\u00a0<\/strong>amount of space occupied by an object<\/p>\n<\/div>\n","protected":false},"author":330,"menu_order":3,"template":"","meta":{"pb_show_title":"on","pb_short_title":"2.2 Measurements and Units","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc-sa"},"chapter-type":[],"contributor":[],"license":[54],"class_list":["post-1284","chapter","type-chapter","status-publish","hentry","license-cc-by-nc-sa"],"part":2084,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/pressbooks\/v2\/chapters\/1284","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/wp\/v2\/users\/330"}],"version-history":[{"count":25,"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/pressbooks\/v2\/chapters\/1284\/revisions"}],"predecessor-version":[{"id":4801,"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/pressbooks\/v2\/chapters\/1284\/revisions\/4801"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/pressbooks\/v2\/parts\/2084"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/pressbooks\/v2\/chapters\/1284\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/wp\/v2\/media?parent=1284"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/pressbooks\/v2\/chapter-type?post=1284"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/wp\/v2\/contributor?post=1284"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/wp\/v2\/license?post=1284"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}