{"id":46,"date":"2022-12-08T17:05:08","date_gmt":"2022-12-08T22:05:08","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/math024\/chapter\/part-of-the-whole-thing\/"},"modified":"2025-07-15T22:09:29","modified_gmt":"2025-07-16T02:09:29","slug":"part-of-the-whole-thing","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/math024\/chapter\/part-of-the-whole-thing\/","title":{"raw":"Topic A: Part of the Whole Thing","rendered":"Topic A: Part of the Whole Thing"},"content":{"raw":"This is the beginning of an adventure with numbers that represent part of the whole thing. These numbers can be shown in a few different ways:\r\n<table class=\"grid aligncenter\" style=\"border-collapse: collapse;width: 50%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<th style=\"width: 50%\" scope=\"col\">Fraction name<\/th>\r\n<th style=\"width: 50%\" scope=\"col\">Example<\/th>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;text-align: center\">Decimal fraction<\/td>\r\n<td style=\"width: 50%;text-align: center\">0.50<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;text-align: center\">Common fraction<\/td>\r\n<td style=\"width: 50%;text-align: center\">[latex]\\dfrac{1}{2}[\/latex] or [latex]\\dfrac{50}{100}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;text-align: center\">Percent fraction<\/td>\r\n<td style=\"width: 50%;text-align: center\">50%<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWhen we talk about fractions in any of the three ways listed above, we are talking about numbers in relation to the whole thing. What do we mean by \u201cthe whole thing\u201d? We mean one complete thing.\r\n\r\nAn example would be one full jug of juice. That is 1 whole thing.\r\n\r\n<img class=\"aligncenter wp-image-25\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2022\/12\/image7.png\" alt=\"A full jug of juice.\" width=\"100\" height=\"182\" \/>\r\n\r\nOnce someone starts taking some juice, less than the whole thing remains. Now, half of the juice is gone.<img class=\"aligncenter wp-image-26\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/image5-e1670541661447.png\" alt=\"A jug of juice that is half empty.\" width=\"100\" height=\"189\" \/>The remaining amount can be written as\r\n<ul>\r\n \t<li>half of one whole thing<\/li>\r\n \t<li>0.5<\/li>\r\n \t<li>\u00bd<\/li>\r\n \t<li>50%<\/li>\r\n<\/ul>\r\nNow almost all the juice has been taken.\r\n\r\n<img class=\"aligncenter wp-image-27\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/image6.png\" alt=\"A jug of juice with only one quarter of juice left.\" width=\"100\" height=\"196\" \/>The remaining amount can be written as\r\n<ul>\r\n \t<li>0.25<\/li>\r\n \t<li>\u00bc<\/li>\r\n \t<li>25%<\/li>\r\n<\/ul>\r\nNow there are two full jugs of juice. This shows <em>two <\/em>whole things.\r\n\r\n<img class=\"aligncenter wp-image-28\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/2-jugs.png\" alt=\"\" width=\"224\" height=\"196\" \/>\r\n\r\nA fraction does not tell us much unless we know what the fraction is part of\u2014we need to know exactly what the whole thing is! If someone says to you, \u201cSure, let\u2019s go! I still have half!\u201d you really need to know, \u201cHalf of what?\u201d\r\n\r\nThe answer could be [latex]\\frac{1}{2}[\/latex] a tank of gas, or [latex]\\frac{1}{2}[\/latex] a paycheque, or [latex]\\frac{1}{2}[\/latex] a vacation, or [latex]\\frac{1}{2}[\/latex] an hour.\r\n<div class=\"textbox\">Fractions have meaning only when we understand the whole thing.<\/div>\r\n<h1>Decimal Fractions<\/h1>\r\nDecimal fractions are one way to consider parts of the whole thing. The whole thing = 1.\r\n\r\nYou use decimal fractions every time you think about money. The dollars are written as whole numbers and the cents are written as a decimal fraction of a dollar.\r\n\r\n<img class=\"aligncenter wp-image-29 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/parts-of-a-dollar.jpg\" alt=\"With 4 dollars and 75 cents, there are 4 whole dollars ar 0.75 part of a dollar.\" width=\"367\" height=\"160\" \/>A decimal fraction has a decimal point that separates the whole number from the fraction. The decimal point looks like this:\u00a0\u00a0 <img class=\"alignnone wp-image-46\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/image26.png\" alt=\"A decimal point, which looks like a dot or a period.\" width=\"5\" height=\"5\" \/>\r\n\r\nA whole pizza might be divided into eight pieces, or ten pieces, or twelve pieces. However, for decimal fractions the whole is always divided into ten pieces, which are called tenths. This is because we use a decimal system based on the number ten (\"deci\" is the Latin word for tenth). The tenths are also divided into ten pieces to make hundredths. And then the hundredths are divided by ten to make thousandths, and so on.\r\n\r\nDecimal fractions are often used in our daily lives, especially for money and measurement. For example:\r\n<ul>\r\n \t<li>The total was $12.24.<\/li>\r\n \t<li>It is 3.5 kilometres from my house to the store.<\/li>\r\n \t<li>It costs $1.99 per kilogram for apples.<\/li>\r\n \t<li>She caught a 4.8 kilogram salmon.<\/li>\r\n<\/ul>\r\n<p style=\"text-align: left\">You will be working with decimal fractions in the first two units of this book.<\/p>\r\n\r\n<table class=\"no-border aligncenter\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\"><img class=\"aligncenter wp-image-31\" style=\"margin-top: 0.5em;margin-bottom: 0.5em;text-align: center;font-size: 18.6667px\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/image9.jpeg\" alt=\"A tag for beef sausage that lists the price as $7.04.\" width=\"300\" height=\"163\" \/><\/td>\r\n<td style=\"width: 50%\" rowspan=\"2\"><img class=\"wp-image-33 alignnone\" style=\"margin-top: 0.5em;margin-bottom: 0.5em;text-align: center;font-size: 18.6667px\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/image8-e1670543569844.jpeg\" alt=\"A Safeway flyer showing the price of different types of grocery items. For example, cheese is $6.99.\" width=\"300\" height=\"592\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\"><img class=\"aligncenter wp-image-32\" style=\"margin-top: 0.5em;margin-bottom: 0.5em;text-align: center;font-size: 18.6667px\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/image10.jpeg\" alt=\"The price of gas at a gas station is showing as $1.229.\" width=\"300\" height=\"169\" \/><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h1>Common Fractions<\/h1>\r\n[pb_glossary id=\"164\"]Common fractions[\/pb_glossary] are a second way we will work with parts of the whole thing.\r\n\r\nThey are written with two numbers, one above the other, with a line in between. The line may be straight, or it may be on an angle.\r\n<p style=\"text-align: center\">[latex]\\frac{3}{4}[\/latex] or <strong>\u00be<\/strong><\/p>\r\nThe [pb_glossary id=\"195\"]numerator[\/pb_glossary] is the top number in a common fraction. The numerator tells how many parts. The [pb_glossary id=\"166\"]denominator[\/pb_glossary] is the bottom number. The denominator tells how many equal parts there are in the whole thing.\r\n\r\n<img class=\"aligncenter wp-image-34 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/3_4.png\" alt=\"In the common fraction 3 over 4, 3 is the numerator and 4 is the denominator.\" width=\"334\" height=\"101\" \/>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example A<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n<img class=\"alignright wp-image-35\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/image15.jpeg\" alt=\"\" width=\"200\" height=\"122\" \/>The whole thing is 1 pizza. This pizza has been cut into 8 equal pieces. The denominator is 8.\r\n\r\nAs a fraction, the whole thing is [latex]\\tfrac{8}{8}[\/latex] (eight-eigths).\r\n\r\nIf I ate 3 pieces, that would be [latex]\\tfrac{3}{8}[\/latex] of the pizza.\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox\"><a href=\"https:\/\/opentextbc.ca\/alfm5\/\"><em>Adult Literacy Fundamental Mathematics: Book 5<\/em><\/a> explains more about common fractions.<\/div>\r\n<div>\r\n\r\nHere are some things to keep in mind while you complete the following exercise:\r\n<ul>\r\n \t<li>[latex]\\text{one quarter}=0.25=\\frac{1}{4}[\/latex]<\/li>\r\n \t<li>[latex]\\text{one third}= 0.333.. =\\frac{1}{3}[\/latex]<\/li>\r\n \t<li>[latex]\\text{one half}=0.5=\\frac{1}{2}[\/latex]<\/li>\r\n \t<li>[latex]\\text{two thirds}= 0.666...=\\frac{2}{3}[\/latex]<\/li>\r\n \t<li>[latex]\\text{three quarters}=0.75=\\frac{3}{4}[\/latex]<\/li>\r\n<\/ul>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nLook at the pictures and use a fraction to answer the questions.\r\n<ol type=\"A\">\r\n \t<li>How much gas is left?\r\n<ol type=\"a\">\r\n \t<li><img class=\"wp-image-36 alignnone\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/image20.jpeg\" alt=\"A gas guage with the needle in the middle between empty and full.\" width=\"100\" height=\"88\" \/><\/li>\r\n \t<li><img class=\"wp-image-37 size-full alignnone\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/image19.jpeg\" alt=\"A gas guage with the needle pointing at the a mark between half and empty.\" width=\"101\" height=\"160\" \/><\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Do you want more coffee?\r\n<ol type=\"a\">\r\n \t<li>\r\n\r\n[caption id=\"attachment_38\" align=\"alignnone\" width=\"200\"]<img class=\"wp-image-38\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/Full-coffee-cup.jpg\" alt=\"A nearly full coffee cup.\" width=\"200\" height=\"177\" \/> No thanks, I still have ______ of a cup.[\/caption]<\/li>\r\n \t<li>\r\n\r\n[caption id=\"attachment_39\" align=\"alignnone\" width=\"200\"]<img class=\"wp-image-39\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/Half-full-coffee-cup.jpg\" alt=\"A coffee cup that is half full.\" width=\"200\" height=\"166\" \/> Sure, I only have ______ a cup.[\/caption]<\/li>\r\n \t<li>\r\n\r\n[caption id=\"attachment_40\" align=\"alignnone\" width=\"200\"]<img class=\"wp-image-40\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/Nearly-empty-coffee-cup.jpg\" alt=\"A coffee cup that is nearly empty.\" width=\"200\" height=\"162\" \/> Yes please, I'm down to _______ of a cup.[\/caption]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Do we need more juice?\r\n\r\n[caption id=\"attachment_41\" align=\"aligncenter\" width=\"125\"]<img class=\"wp-image-41 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/image6-1.png\" alt=\"A jug of juice with less than half left.\" width=\"125\" height=\"245\" \/> Yes, there is just _____ of the juice.[\/caption]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 1\r\n<\/strong>\r\n\r\nAnswers may differ because the fraction is approximate. Ask your instructor to check any different answers.\r\n<ol type=\"A\">\r\n \t<li>Gas\r\n<ol type=\"a\">\r\n \t<li>[latex]\\tfrac{1}{2}[\/latex] or [latex]\\frac{2}{4}[\/latex] or 0.5<\/li>\r\n \t<li>[latex]\\tfrac{1}{4}[\/latex] or 0.25<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Coffee\r\n<ol type=\"a\">\r\n \t<li>[latex]\\tfrac{3}{4}[\/latex] or 0.75<\/li>\r\n \t<li>[latex]\\tfrac{1}{2}[\/latex] or 0.5<\/li>\r\n \t<li>[latex]\\tfrac{1}{4}[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Juice - [latex]\\tfrac{1}{3}[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Fractions as a Percent<\/h1>\r\nA third and useful way to think about parts of the whole thing is as a [pb_glossary id=\"198\"]percent[\/pb_glossary].\r\n\r\nPercent fractions are written with a number and a percent sign.\r\n<p style=\"text-align: center\"><strong>1%\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 12%\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 50%\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 99%<\/strong><\/p>\r\nIn percent fractions, there is always a denominator of 100. That makes the arithmetic much easier and helps us to understand the fraction.\r\n\r\nFor example, if you got [latex]\\tfrac{14}{20}[\/latex] on a test last week, and [latex]\\tfrac{13}{17}[\/latex] on a test this week, it is hard to get a sense of how you are doing. But if you know you got 70% last week and 76% this week, it is easier to see your improvement.\r\n\r\nIn percent fractions, the whole thing is 100% so 100% equals 1.\r\n\r\nStatistics and general information are often reported in percent fractions.\r\n\r\n<img class=\"aligncenter wp-image-42 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/landfill-pie-chart.png\" alt=\"A pie chart showing the percentage of different types of materials that end up in the Comox Calley landfill.\" width=\"356\" height=\"270\" \/><img class=\"aligncenter wp-image-43 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/security-gic.png\" alt=\"Security G.I.C. plus. Minimum return 2%, maximum return 9%.\" width=\"249\" height=\"180\" \/>\r\n\r\n<img class=\"aligncenter wp-image-44 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/image16.png\" alt=\"A weather notice showing 40 percent chance of rain.\" width=\"225\" height=\"225\" \/>\r\n<div>\r\n<div class=\"textbox\">You will learn to work with fractions as a percent in <a href=\"https:\/\/opentextbc.ca\/alfm6\/\"><em>Adult Literacy Fundamental Mathematics: Book 6<\/em><\/a>. We hope you enjoy the challenge!<\/div>\r\n<\/div>\r\n<h1>What is a Decimal Fraction?<\/h1>\r\nAs you know, fractions describe part of the whole thing. And as you also know, 1 (the whole thing) can be many things. For example, it can be:\r\n<ul class=\"twocolumn\">\r\n \t<li>1 dollar<\/li>\r\n \t<li>1 city<\/li>\r\n \t<li>1 school<\/li>\r\n \t<li>1 pay cheque<\/li>\r\n \t<li>1 year<\/li>\r\n \t<li>1 second<\/li>\r\n \t<li>1 loaf of bread<\/li>\r\n \t<li>1 ferry ride<\/li>\r\n \t<li>etc.<\/li>\r\n<\/ul>\r\nA decimal might represent part of a year, part of the population of Canada, part of an hour, or part of anything.\r\n\r\nDecimal fractions are different from common fractions in several ways:\r\n<ul>\r\n \t<li>A decimal point separates whole numbers from the fraction.\r\n[latex]\\dfrac{1}{10} = 0.1 [\/latex] \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 [latex]\\dfrac{34}{100} = 0.34[\/latex]\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0 [latex]\\dfrac{5}{10} = 0.5[\/latex]<\/li>\r\n \t<li>In a decimal fraction, there is no denominator.<img class=\"aligncenter wp-image-45 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/image25.jpeg\" alt=\"In 1 over 8, 8 is the denominator. In 3 over 4, 4 is the denominator.\" width=\"630\" height=\"101\" \/><\/li>\r\n<\/ul>\r\n<div>\r\n\r\nWe tell the size of the denominator by looking at how many numerals are placed after the decimal point.\r\n\r\nDecimal fraction denominators are always ten or ten multiplied by tens. Decimal means \"based on the number ten\".\r\n\r\n<\/div>\r\n[latex]\\large\\begin{array}{ll}\r\n0.4&amp;\\text{has a denominator of 10}\\\\\r\n0.44&amp;\\text{has a denominator of 100}\\\\\r\n0.444&amp;\\text{has a denominator of 1 000}\\\\\r\n0.4444&amp;\\text{has a denominator of 10 000}\\\\\r\n0.44444&amp;\\text{has a denominator of 100 000}\\\\\r\n0.444444&amp;\\text{has a denominator of 1 000 000}\\\\\r\n\\end{array}[\/latex]\r\n\r\nA whole number and a decimal can be written together. This is called a [pb_glossary id=\"188\"]mixed decimal[\/pb_glossary].\r\n<p style=\"text-align: center\"><strong>4.35\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 100.47\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 $12.39<\/strong><\/p>\r\nEvery whole number has a decimal point after it, even though we usually do not bother to write the decimal point unless apart of the whole (fraction) follows the whole number.\r\n\r\nWe can also put zeros to the right of the decimal point of any whole number without changing its value. Get used to thinking of a decimal point after every whole number!\r\n\r\n[latex]\\begin{array}{ccrcl}\r\n3&amp;=&amp;3.&amp;=&amp;3.0000000\\\\\r\n275&amp;=&amp;275.&amp;=&amp;275.0\\\\\r\n100&amp;=&amp;100.&amp;=&amp;100.0000000000\\\\\r\n$8&amp;=&amp;$8.&amp;=&amp;$8.00\\end{array}[\/latex]\r\n<div class=\"textbox\">Tip: In math, we use the word decimal to mean decimal fraction. \u00a0In the rest of this book, you will see the word decimal, and it will mean decimal fraction.<\/div>","rendered":"<p>This is the beginning of an adventure with numbers that represent part of the whole thing. These numbers can be shown in a few different ways:<\/p>\n<table class=\"grid aligncenter\" style=\"border-collapse: collapse;width: 50%\">\n<tbody>\n<tr>\n<th style=\"width: 50%\" scope=\"col\">Fraction name<\/th>\n<th style=\"width: 50%\" scope=\"col\">Example<\/th>\n<\/tr>\n<tr>\n<td style=\"width: 50%;text-align: center\">Decimal fraction<\/td>\n<td style=\"width: 50%;text-align: center\">0.50<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;text-align: center\">Common fraction<\/td>\n<td style=\"width: 50%;text-align: center\">[latex]\\dfrac{1}{2}[\/latex] or [latex]\\dfrac{50}{100}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;text-align: center\">Percent fraction<\/td>\n<td style=\"width: 50%;text-align: center\">50%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>When we talk about fractions in any of the three ways listed above, we are talking about numbers in relation to the whole thing. What do we mean by \u201cthe whole thing\u201d? We mean one complete thing.<\/p>\n<p>An example would be one full jug of juice. That is 1 whole thing.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-25\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2022\/12\/image7.png\" alt=\"A full jug of juice.\" width=\"100\" height=\"182\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2022\/12\/image7.png 282w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2022\/12\/image7-165x300.png 165w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2022\/12\/image7-65x118.png 65w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2022\/12\/image7-225x409.png 225w\" sizes=\"auto, (max-width: 100px) 100vw, 100px\" \/><\/p>\n<p>Once someone starts taking some juice, less than the whole thing remains. Now, half of the juice is gone.<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-26\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/image5-e1670541661447.png\" alt=\"A jug of juice that is half empty.\" width=\"100\" height=\"189\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image5-e1670541661447.png 133w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image5-e1670541661447-65x123.png 65w\" sizes=\"auto, (max-width: 100px) 100vw, 100px\" \/>The remaining amount can be written as<\/p>\n<ul>\n<li>half of one whole thing<\/li>\n<li>0.5<\/li>\n<li>\u00bd<\/li>\n<li>50%<\/li>\n<\/ul>\n<p>Now almost all the juice has been taken.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-27\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/image6.png\" alt=\"A jug of juice with only one quarter of juice left.\" width=\"100\" height=\"196\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image6.png 125w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image6-65x127.png 65w\" sizes=\"auto, (max-width: 100px) 100vw, 100px\" \/>The remaining amount can be written as<\/p>\n<ul>\n<li>0.25<\/li>\n<li>\u00bc<\/li>\n<li>25%<\/li>\n<\/ul>\n<p>Now there are two full jugs of juice. This shows <em>two <\/em>whole things.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-28\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/2-jugs.png\" alt=\"\" width=\"224\" height=\"196\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/2-jugs.png 261w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/2-jugs-65x57.png 65w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/2-jugs-225x197.png 225w\" sizes=\"auto, (max-width: 224px) 100vw, 224px\" \/><\/p>\n<p>A fraction does not tell us much unless we know what the fraction is part of\u2014we need to know exactly what the whole thing is! If someone says to you, \u201cSure, let\u2019s go! I still have half!\u201d you really need to know, \u201cHalf of what?\u201d<\/p>\n<p>The answer could be [latex]\\frac{1}{2}[\/latex] a tank of gas, or [latex]\\frac{1}{2}[\/latex] a paycheque, or [latex]\\frac{1}{2}[\/latex] a vacation, or [latex]\\frac{1}{2}[\/latex] an hour.<\/p>\n<div class=\"textbox\">Fractions have meaning only when we understand the whole thing.<\/div>\n<h1>Decimal Fractions<\/h1>\n<p>Decimal fractions are one way to consider parts of the whole thing. The whole thing = 1.<\/p>\n<p>You use decimal fractions every time you think about money. The dollars are written as whole numbers and the cents are written as a decimal fraction of a dollar.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-29 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/parts-of-a-dollar.jpg\" alt=\"With 4 dollars and 75 cents, there are 4 whole dollars ar 0.75 part of a dollar.\" width=\"367\" height=\"160\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/parts-of-a-dollar.jpg 367w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/parts-of-a-dollar-300x131.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/parts-of-a-dollar-65x28.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/parts-of-a-dollar-225x98.jpg 225w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/parts-of-a-dollar-350x153.jpg 350w\" sizes=\"auto, (max-width: 367px) 100vw, 367px\" \/>A decimal fraction has a decimal point that separates the whole number from the fraction. The decimal point looks like this:\u00a0\u00a0 <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-46\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/image26.png\" alt=\"A decimal point, which looks like a dot or a period.\" width=\"5\" height=\"5\" \/><\/p>\n<p>A whole pizza might be divided into eight pieces, or ten pieces, or twelve pieces. However, for decimal fractions the whole is always divided into ten pieces, which are called tenths. This is because we use a decimal system based on the number ten (&#8220;deci&#8221; is the Latin word for tenth). The tenths are also divided into ten pieces to make hundredths. And then the hundredths are divided by ten to make thousandths, and so on.<\/p>\n<p>Decimal fractions are often used in our daily lives, especially for money and measurement. For example:<\/p>\n<ul>\n<li>The total was $12.24.<\/li>\n<li>It is 3.5 kilometres from my house to the store.<\/li>\n<li>It costs $1.99 per kilogram for apples.<\/li>\n<li>She caught a 4.8 kilogram salmon.<\/li>\n<\/ul>\n<p style=\"text-align: left\">You will be working with decimal fractions in the first two units of this book.<\/p>\n<table class=\"no-border aligncenter\">\n<tbody>\n<tr>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-31\" style=\"margin-top: 0.5em;margin-bottom: 0.5em;text-align: center;font-size: 18.6667px\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/image9.jpeg\" alt=\"A tag for beef sausage that lists the price as $7.04.\" width=\"300\" height=\"163\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image9.jpeg 382w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image9-300x163.jpeg 300w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image9-65x35.jpeg 65w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image9-225x122.jpeg 225w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image9-350x190.jpeg 350w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/td>\n<td style=\"width: 50%\" rowspan=\"2\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-33 alignnone\" style=\"margin-top: 0.5em;margin-bottom: 0.5em;text-align: center;font-size: 18.6667px\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/image8-e1670543569844.jpeg\" alt=\"A Safeway flyer showing the price of different types of grocery items. For example, cheese is $6.99.\" width=\"300\" height=\"592\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image8-e1670543569844.jpeg 399w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image8-e1670543569844-152x300.jpeg 152w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image8-e1670543569844-65x128.jpeg 65w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image8-e1670543569844-225x444.jpeg 225w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image8-e1670543569844-350x690.jpeg 350w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-32\" style=\"margin-top: 0.5em;margin-bottom: 0.5em;text-align: center;font-size: 18.6667px\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/image10.jpeg\" alt=\"The price of gas at a gas station is showing as $1.229.\" width=\"300\" height=\"169\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image10.jpeg 720w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image10-300x169.jpeg 300w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image10-65x37.jpeg 65w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image10-225x127.jpeg 225w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image10-350x197.jpeg 350w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Common Fractions<\/h1>\n<p><a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_46_164\">Common fractions<\/a> are a second way we will work with parts of the whole thing.<\/p>\n<p>They are written with two numbers, one above the other, with a line in between. The line may be straight, or it may be on an angle.<\/p>\n<p style=\"text-align: center\">[latex]\\frac{3}{4}[\/latex] or <strong>\u00be<\/strong><\/p>\n<p>The <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_46_195\">numerator<\/a> is the top number in a common fraction. The numerator tells how many parts. The <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_46_166\">denominator<\/a> is the bottom number. The denominator tells how many equal parts there are in the whole thing.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-34 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/3_4.png\" alt=\"In the common fraction 3 over 4, 3 is the numerator and 4 is the denominator.\" width=\"334\" height=\"101\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/3_4.png 334w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/3_4-300x91.png 300w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/3_4-65x20.png 65w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/3_4-225x68.png 225w\" sizes=\"auto, (max-width: 334px) 100vw, 334px\" \/><\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example A<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignright wp-image-35\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/image15.jpeg\" alt=\"\" width=\"200\" height=\"122\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image15.jpeg 1024w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image15-300x183.jpeg 300w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image15-768x468.jpeg 768w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image15-65x40.jpeg 65w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image15-225x137.jpeg 225w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image15-350x213.jpeg 350w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/>The whole thing is 1 pizza. This pizza has been cut into 8 equal pieces. The denominator is 8.<\/p>\n<p>As a fraction, the whole thing is [latex]\\tfrac{8}{8}[\/latex] (eight-eigths).<\/p>\n<p>If I ate 3 pieces, that would be [latex]\\tfrac{3}{8}[\/latex] of the pizza.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox\"><a href=\"https:\/\/opentextbc.ca\/alfm5\/\"><em>Adult Literacy Fundamental Mathematics: Book 5<\/em><\/a> explains more about common fractions.<\/div>\n<div>\n<p>Here are some things to keep in mind while you complete the following exercise:<\/p>\n<ul>\n<li>[latex]\\text{one quarter}=0.25=\\frac{1}{4}[\/latex]<\/li>\n<li>[latex]\\text{one third}= 0.333.. =\\frac{1}{3}[\/latex]<\/li>\n<li>[latex]\\text{one half}=0.5=\\frac{1}{2}[\/latex]<\/li>\n<li>[latex]\\text{two thirds}= 0.666...=\\frac{2}{3}[\/latex]<\/li>\n<li>[latex]\\text{three quarters}=0.75=\\frac{3}{4}[\/latex]<\/li>\n<\/ul>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Look at the pictures and use a fraction to answer the questions.<\/p>\n<ol type=\"A\">\n<li>How much gas is left?\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-36 alignnone\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/image20.jpeg\" alt=\"A gas guage with the needle in the middle between empty and full.\" width=\"100\" height=\"88\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image20.jpeg 324w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image20-300x264.jpeg 300w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image20-65x57.jpeg 65w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image20-225x198.jpeg 225w\" sizes=\"auto, (max-width: 100px) 100vw, 100px\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-37 size-full alignnone\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/image19.jpeg\" alt=\"A gas guage with the needle pointing at the a mark between half and empty.\" width=\"101\" height=\"160\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image19.jpeg 101w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image19-65x103.jpeg 65w\" sizes=\"auto, (max-width: 101px) 100vw, 101px\" \/><\/li>\n<\/ol>\n<\/li>\n<li>Do you want more coffee?\n<ol type=\"a\">\n<li>\n<figure id=\"attachment_38\" aria-describedby=\"caption-attachment-38\" style=\"width: 200px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-38\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/Full-coffee-cup.jpg\" alt=\"A nearly full coffee cup.\" width=\"200\" height=\"177\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/Full-coffee-cup.jpg 256w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/Full-coffee-cup-65x57.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/Full-coffee-cup-225x199.jpg 225w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/><figcaption id=\"caption-attachment-38\" class=\"wp-caption-text\">No thanks, I still have ______ of a cup.<\/figcaption><\/figure>\n<\/li>\n<li>\n<figure id=\"attachment_39\" aria-describedby=\"caption-attachment-39\" style=\"width: 200px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-39\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/Half-full-coffee-cup.jpg\" alt=\"A coffee cup that is half full.\" width=\"200\" height=\"166\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/Half-full-coffee-cup.jpg 259w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/Half-full-coffee-cup-65x54.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/Half-full-coffee-cup-225x187.jpg 225w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/><figcaption id=\"caption-attachment-39\" class=\"wp-caption-text\">Sure, I only have ______ a cup.<\/figcaption><\/figure>\n<\/li>\n<li>\n<figure id=\"attachment_40\" aria-describedby=\"caption-attachment-40\" style=\"width: 200px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-40\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/Nearly-empty-coffee-cup.jpg\" alt=\"A coffee cup that is nearly empty.\" width=\"200\" height=\"162\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/Nearly-empty-coffee-cup.jpg 257w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/Nearly-empty-coffee-cup-65x53.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/Nearly-empty-coffee-cup-225x182.jpg 225w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/><figcaption id=\"caption-attachment-40\" class=\"wp-caption-text\">Yes please, I&#8217;m down to _______ of a cup.<\/figcaption><\/figure>\n<\/li>\n<\/ol>\n<\/li>\n<li>Do we need more juice?<br \/>\n<figure id=\"attachment_41\" aria-describedby=\"caption-attachment-41\" style=\"width: 125px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-41 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/image6-1.png\" alt=\"A jug of juice with less than half left.\" width=\"125\" height=\"245\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image6-1.png 125w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image6-1-65x127.png 65w\" sizes=\"auto, (max-width: 125px) 100vw, 125px\" \/><figcaption id=\"caption-attachment-41\" class=\"wp-caption-text\">Yes, there is just _____ of the juice.<\/figcaption><\/figure>\n<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 1<br \/>\n<\/strong><\/p>\n<p>Answers may differ because the fraction is approximate. Ask your instructor to check any different answers.<\/p>\n<ol type=\"A\">\n<li>Gas\n<ol type=\"a\">\n<li>[latex]\\tfrac{1}{2}[\/latex] or [latex]\\frac{2}{4}[\/latex] or 0.5<\/li>\n<li>[latex]\\tfrac{1}{4}[\/latex] or 0.25<\/li>\n<\/ol>\n<\/li>\n<li>Coffee\n<ol type=\"a\">\n<li>[latex]\\tfrac{3}{4}[\/latex] or 0.75<\/li>\n<li>[latex]\\tfrac{1}{2}[\/latex] or 0.5<\/li>\n<li>[latex]\\tfrac{1}{4}[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>Juice &#8211; [latex]\\tfrac{1}{3}[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<h1>Fractions as a Percent<\/h1>\n<p>A third and useful way to think about parts of the whole thing is as a <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_46_198\">percent<\/a>.<\/p>\n<p>Percent fractions are written with a number and a percent sign.<\/p>\n<p style=\"text-align: center\"><strong>1%\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 12%\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 50%\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 99%<\/strong><\/p>\n<p>In percent fractions, there is always a denominator of 100. That makes the arithmetic much easier and helps us to understand the fraction.<\/p>\n<p>For example, if you got [latex]\\tfrac{14}{20}[\/latex] on a test last week, and [latex]\\tfrac{13}{17}[\/latex] on a test this week, it is hard to get a sense of how you are doing. But if you know you got 70% last week and 76% this week, it is easier to see your improvement.<\/p>\n<p>In percent fractions, the whole thing is 100% so 100% equals 1.<\/p>\n<p>Statistics and general information are often reported in percent fractions.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-42 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/landfill-pie-chart.png\" alt=\"A pie chart showing the percentage of different types of materials that end up in the Comox Calley landfill.\" width=\"356\" height=\"270\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/landfill-pie-chart.png 356w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/landfill-pie-chart-300x228.png 300w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/landfill-pie-chart-65x49.png 65w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/landfill-pie-chart-225x171.png 225w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/landfill-pie-chart-350x265.png 350w\" sizes=\"auto, (max-width: 356px) 100vw, 356px\" \/><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-43 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/security-gic.png\" alt=\"Security G.I.C. plus. Minimum return 2%, maximum return 9%.\" width=\"249\" height=\"180\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/security-gic.png 249w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/security-gic-65x47.png 65w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/security-gic-225x163.png 225w\" sizes=\"auto, (max-width: 249px) 100vw, 249px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-44 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/image16.png\" alt=\"A weather notice showing 40 percent chance of rain.\" width=\"225\" height=\"225\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image16.png 225w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image16-150x150.png 150w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image16-65x65.png 65w\" sizes=\"auto, (max-width: 225px) 100vw, 225px\" \/><\/p>\n<div>\n<div class=\"textbox\">You will learn to work with fractions as a percent in <a href=\"https:\/\/opentextbc.ca\/alfm6\/\"><em>Adult Literacy Fundamental Mathematics: Book 6<\/em><\/a>. We hope you enjoy the challenge!<\/div>\n<\/div>\n<h1>What is a Decimal Fraction?<\/h1>\n<p>As you know, fractions describe part of the whole thing. And as you also know, 1 (the whole thing) can be many things. For example, it can be:<\/p>\n<ul class=\"twocolumn\">\n<li>1 dollar<\/li>\n<li>1 city<\/li>\n<li>1 school<\/li>\n<li>1 pay cheque<\/li>\n<li>1 year<\/li>\n<li>1 second<\/li>\n<li>1 loaf of bread<\/li>\n<li>1 ferry ride<\/li>\n<li>etc.<\/li>\n<\/ul>\n<p>A decimal might represent part of a year, part of the population of Canada, part of an hour, or part of anything.<\/p>\n<p>Decimal fractions are different from common fractions in several ways:<\/p>\n<ul>\n<li>A decimal point separates whole numbers from the fraction.<br \/>\n[latex]\\dfrac{1}{10} = 0.1[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 [latex]\\dfrac{34}{100} = 0.34[\/latex]\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0 [latex]\\dfrac{5}{10} = 0.5[\/latex]<\/li>\n<li>In a decimal fraction, there is no denominator.<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-45 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2382\/2025\/01\/image25.jpeg\" alt=\"In 1 over 8, 8 is the denominator. In 3 over 4, 4 is the denominator.\" width=\"630\" height=\"101\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image25.jpeg 630w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image25-300x48.jpeg 300w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image25-65x10.jpeg 65w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image25-225x36.jpeg 225w, https:\/\/pressbooks.bccampus.ca\/math024\/wp-content\/uploads\/sites\/2382\/2025\/01\/image25-350x56.jpeg 350w\" sizes=\"auto, (max-width: 630px) 100vw, 630px\" \/><\/li>\n<\/ul>\n<div>\n<p>We tell the size of the denominator by looking at how many numerals are placed after the decimal point.<\/p>\n<p>Decimal fraction denominators are always ten or ten multiplied by tens. Decimal means &#8220;based on the number ten&#8221;.<\/p>\n<\/div>\n<p>[latex]\\large\\begin{array}{ll}  0.4&\\text{has a denominator of 10}\\\\  0.44&\\text{has a denominator of 100}\\\\  0.444&\\text{has a denominator of 1 000}\\\\  0.4444&\\text{has a denominator of 10 000}\\\\  0.44444&\\text{has a denominator of 100 000}\\\\  0.444444&\\text{has a denominator of 1 000 000}\\\\  \\end{array}[\/latex]<\/p>\n<p>A whole number and a decimal can be written together. This is called a <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_46_188\">mixed decimal<\/a>.<\/p>\n<p style=\"text-align: center\"><strong>4.35\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 100.47\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 $12.39<\/strong><\/p>\n<p>Every whole number has a decimal point after it, even though we usually do not bother to write the decimal point unless apart of the whole (fraction) follows the whole number.<\/p>\n<p>We can also put zeros to the right of the decimal point of any whole number without changing its value. Get used to thinking of a decimal point after every whole number!<\/p>\n<p>[latex]\\begin{array}{ccrcl}  3&=&3.&=&3.0000000\\\\  275&=&275.&=&275.0\\\\  100&=&100.&=&100.0000000000\\\\  $8&=&$8.&=&$8.00\\end{array}[\/latex]<\/p>\n<div class=\"textbox\">Tip: In math, we use the word decimal to mean decimal fraction. \u00a0In the rest of this book, you will see the word decimal, and it will mean decimal fraction.<\/div>\n<div class=\"glossary\"><span class=\"screen-reader-text\" id=\"definition\">definition<\/span><template id=\"term_46_164\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_46_164\"><div tabindex=\"-1\"><p>e.g., \u2154, \u00b3\u2044\u2087 , \u2074\u2079\u2044\u2085\u2080<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_46_195\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_46_195\"><div tabindex=\"-1\"><p>The top number in a common fraction; the numerator tells how many parts of the whole thing are being considered.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_46_166\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_46_166\"><div tabindex=\"-1\"><p>The bottom number in a common fraction; tells into how many equal parts the whole thing has been divided.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_46_198\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_46_198\"><div tabindex=\"-1\"><p>For every one hundred.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_46_188\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_46_188\"><div tabindex=\"-1\"><p>A whole number and a decimal fraction. 1.75<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><\/div>","protected":false},"author":999,"menu_order":1,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[48],"contributor":[],"license":[],"class_list":["post-46","chapter","type-chapter","status-publish","hentry","chapter-type-standard"],"part":24,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/pressbooks\/v2\/chapters\/46","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/wp\/v2\/users\/999"}],"version-history":[{"count":5,"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/pressbooks\/v2\/chapters\/46\/revisions"}],"predecessor-version":[{"id":252,"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/pressbooks\/v2\/chapters\/46\/revisions\/252"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/pressbooks\/v2\/parts\/24"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/pressbooks\/v2\/chapters\/46\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/wp\/v2\/media?parent=46"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/pressbooks\/v2\/chapter-type?post=46"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/wp\/v2\/contributor?post=46"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/wp\/v2\/license?post=46"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}