{"id":203,"date":"2022-10-06T15:28:34","date_gmt":"2022-10-06T19:28:34","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/math025\/chapter\/topic-b-comparing-fractions-decimals\/"},"modified":"2025-06-28T00:57:14","modified_gmt":"2025-06-28T04:57:14","slug":"topic-b-comparing-fractions-decimals","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/math025\/chapter\/topic-b-comparing-fractions-decimals\/","title":{"raw":"Topic B: Comparing Fractions &amp; Decimals","rendered":"Topic B: Comparing Fractions &amp; Decimals"},"content":{"raw":"In Unit 2 you compared simple fractions to simple fractions such as [latex]\\dfrac{1}{2}[\/latex]<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>[latex]\\dfrac{1}{3}[\/latex]\r\n\r\nNow, you are going to be asked to compare fractions with larger and less common denominators such as [latex]\\tfrac{7}{8}[\/latex] and [latex]\\tfrac{17}{28}[\/latex]\r\n<p style=\"text-align: center\">Find the equivalent fractions of both the fractions and then compare.\r\n[latex]\\dfrac{1}{2}\\left(\\dfrac{\u00d73}{\u00d73}\\right) = \\dfrac{3}{6}[\/latex] and [latex]\\dfrac{1}{3}\\left(\\dfrac{\u00d72}{\u00d72}\\right)=\\dfrac{2}{6}[\/latex] so [latex]\\dfrac{3}{6}\u2265\\dfrac{2}{6}[\/latex]<\/p>\r\n<p style=\"text-align: center\">[latex]\\dfrac{7}{8}\\left(\\dfrac{\u00d77}{\u00d77}\\right)=\\dfrac{49}{56}[\/latex] and [latex]\\dfrac{17}{28}\\left(\\dfrac{\u00d72}{\u00d72}\\right)=\\dfrac{34}{56}[\/latex] so [latex]\\dfrac{49}{56}\u2265\\dfrac{34}{56}[\/latex]<\/p>\r\n\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\nChange the fractions to have the same denominators. Decide which is larger. Use &gt; , &lt; , = to mark your answer. There is space below each problem to work out your equivalent fractions.\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>[latex]\\dfrac{1}{4}[\/latex]<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> [latex]\\dfrac{3}{5}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{5}{8}[\/latex]<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span>[latex]\\dfrac{3}{4}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{1}{5}[\/latex]<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> [latex]\\dfrac{2}{3}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{2}{3}[\/latex]<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> [latex]\\dfrac{3}{4}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{49}{56}[\/latex] <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> [latex]\\dfrac{3}{4}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{75}{90}[\/latex] <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> [latex]\\dfrac{10}{11}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{33}{70}[\/latex] <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> [latex]\\dfrac{1}{2}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{1}{3}[\/latex] <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>[latex]\\dfrac{1}{9}[\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise One<\/strong>\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>&lt;<\/li>\r\n \t<li>&lt;<\/li>\r\n \t<li>&lt;<\/li>\r\n \t<li>&lt;<\/li>\r\n \t<li>&gt;<\/li>\r\n \t<li>&lt;<\/li>\r\n \t<li>&lt;<\/li>\r\n \t<li>&gt;<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h1>Comparing Fractions to Decimals and Decimals to Fractions<\/h1>\r\nNow that you know how to convert between fractions and decimals, you are also going to be able to compare them.\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\nWhich is larger: [latex]\\dfrac{3}{8}[\/latex] or 0.125?\r\n<ol>\r\n \t<li>Decide to convert either the fraction into a decimal, or the decimal into a fraction. Let\u2019s pick converting the fraction into a decimal.<\/li>\r\n \t<li>Do the conversion[latex]\\dfrac{3}{8}[\/latex] =[latex]\\begin{array}{r}0.375\\\\ 8\\enclose{longdiv}{3.000}\\\\ 24\\downarrow \\ \\ \\\\ \\hline60\\hspace{0.8em}\\\\56\\downarrow\\\\\\hline40\\hspace{0.1em}\\\\40\\hspace{0.1em}\\\\\\hline\\end{array}[\/latex]\u00a0 \u00a0 \u00a0= 0.375<\/li>\r\n \t<li>Compare\u00a0<span class=\"ui-provider ank b c d e f g h i j k l m n o p q r s t u v w x y z ab ac ae af ag ah ai aj ak\" dir=\"ltr\">[latex]0.375\\underline{\\hspace{0.5em}&gt;\\hspace{0.5em}}0.125[\/latex]<\/span><\/li>\r\n \t<li>Write a math sentence to show your answer: [latex]\\dfrac{3}{8}\\underline{\\hspace{0.5em}&gt;\\hspace{0.5em}}0.125[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example B<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nWhich is larger[latex]\\dfrac{7}{8}[\/latex] or 0.6?\r\n<ol>\r\n \t<li>Pick which you will convert, the decimal into the fraction, or the fraction into the decimal.\u00a0 <strong>Let\u2019s pick converting the decimal this time.<\/strong><\/li>\r\n \t<li>Convert 0.6= [latex]\\dfrac{6}{10}\\left(\\dfrac{ \u00f7 2}{ \u00f7 2}\\right) = \\dfrac{3}{5}[\/latex]<\/li>\r\n \t<li>Compare [latex]\\dfrac{7}{8}[\/latex] to [latex] \\dfrac{3}{5}[\/latex][latex] \\longrightarrow\\dfrac{7}{8}\\left(\\dfrac{ \u00d7 5}{ \u00d7 5}\\right) = \\dfrac{35}{40}[\/latex] ; [latex]\\dfrac{3}{5}\\left(\\dfrac{ \u00d7 8}{ \u00d7 8}\\right) = \\dfrac{24}{40}[\/latex]<\/li>\r\n \t<li>Write a math sentence to show your answer [latex]\\dfrac{7}{8}\\underline{\\hspace{0.5em} &gt;\\hspace{0.5em}}0.6[\/latex]<\/li>\r\n<\/ol>\r\nTIP: You may find that converting the fractions to the decimals could speed things up.\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nCompare\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>0.25 <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>[latex]\\dfrac{1}{5}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{1}{8}[\/latex]<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>\u00a00.8<\/li>\r\n \t<li>[latex]\\dfrac{1}{6}[\/latex]<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>\u00a0 0.125<\/li>\r\n \t<li>0.2<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>[latex]\\dfrac{3}{10}[\/latex]<\/li>\r\n \t<li>0.3725<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>[latex]\\dfrac{2}{3}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{2}{5}[\/latex]<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>0.5<\/li>\r\n \t<li>0.3725<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>[latex]\\dfrac{1}{5}[\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise Two<\/strong>\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>&gt;<\/li>\r\n \t<li>&lt;<\/li>\r\n \t<li>&gt;<\/li>\r\n \t<li>&lt;<\/li>\r\n \t<li>&lt;<\/li>\r\n \t<li>&lt;<\/li>\r\n \t<li>&gt;<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n<strong>Compare the following numbers to each other. Use &gt; or &lt; .<\/strong>\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>0.345<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>[latex]\\dfrac{6}{7}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{1}{1051}[\/latex]<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>0.0032<\/li>\r\n \t<li>0.52<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>[latex]\\dfrac{2}{3}[\/latex]<\/li>\r\n \t<li>0.6894<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>[latex]\\dfrac{103}{278}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{1}{72}[\/latex]<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>[latex]\\dfrac{2}{3}[\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise Three<\/strong>\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>&lt;<\/li>\r\n \t<li>&lt;<\/li>\r\n \t<li>&lt;<\/li>\r\n \t<li>&gt;<\/li>\r\n \t<li>&lt;<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h1>Topic B Self-Test<\/h1>\r\n<strong>Mark \/18\u00a0 Aim 15 \/ 18<\/strong>\r\n<ol type=\"A\">\r\n \t<li>Write as common fractions in lowest terms. (4 marks)\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>3.6<\/li>\r\n \t<li>8.125<\/li>\r\n \t<li>0.75<\/li>\r\n \t<li>0.45<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Write as decimals. Round your answers to 3 decimal places. (4 marks)\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>[latex]\\dfrac{3}{5}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{6}{100}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{3}{8}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{5}{7}[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Compare the following fractions and decimals, use &lt; , or &gt;. (6 marks)\r\n<ol class=\"twocolumn space\" type=\"a\">\r\n \t<li>0.862 <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> [latex]\\dfrac{6}{7}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{3}{14}[\/latex] <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> 0.35<\/li>\r\n \t<li>[latex]\\dfrac{1}{10}[\/latex] <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> \u00a0 0.007<\/li>\r\n \t<li>0.3<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>[latex]\\dfrac{20}{26}[\/latex]<\/li>\r\n \t<li>0.5 <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> [latex]\\dfrac{10}{21}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{89}{90}[\/latex]\u00a0 <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> 0.473<\/li>\r\n \t<li>[latex]\\dfrac{1}{3}[\/latex]\u00a0 <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>[latex]\\dfrac{1}{9}[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Problems. 4 marks\r\n<ol type=\"a\">\r\n \t<li>May babysat for [latex]4 \\tfrac{1}{4} [\/latex] hours. She is paid $4.75 an hour. How much did she earn?<\/li>\r\n \t<li>Diane bought 1.5 litres of milk. Her thirsty kids drank half of it as soon as she got home. How much milk is left?<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<h1>Answers to Topic B Self-Test<\/h1>\r\n<ol type=\"A\">\r\n \t<li>\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>[latex]3\\dfrac{3}{5}[\/latex]<\/li>\r\n \t<li>[latex]8\\dfrac{1}{8}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{3}{4}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{9}{20}[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>0.6<\/li>\r\n \t<li>0.06<\/li>\r\n \t<li>0.375<\/li>\r\n \t<li>0.714<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>&gt;<\/li>\r\n \t<li>&lt;<\/li>\r\n \t<li>&gt;<\/li>\r\n \t<li>&lt;<\/li>\r\n \t<li>&gt;<\/li>\r\n \t<li>&gt;<\/li>\r\n \t<li>&gt;<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>$20.19<\/li>\r\n \t<li>0.75 L<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>","rendered":"<p>In Unit 2 you compared simple fractions to simple fractions such as [latex]\\dfrac{1}{2}[\/latex]<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>[latex]\\dfrac{1}{3}[\/latex]<\/p>\n<p>Now, you are going to be asked to compare fractions with larger and less common denominators such as [latex]\\tfrac{7}{8}[\/latex] and [latex]\\tfrac{17}{28}[\/latex]<\/p>\n<p style=\"text-align: center\">Find the equivalent fractions of both the fractions and then compare.<br \/>\n[latex]\\dfrac{1}{2}\\left(\\dfrac{\u00d73}{\u00d73}\\right) = \\dfrac{3}{6}[\/latex] and [latex]\\dfrac{1}{3}\\left(\\dfrac{\u00d72}{\u00d72}\\right)=\\dfrac{2}{6}[\/latex] so [latex]\\dfrac{3}{6}\u2265\\dfrac{2}{6}[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]\\dfrac{7}{8}\\left(\\dfrac{\u00d77}{\u00d77}\\right)=\\dfrac{49}{56}[\/latex] and [latex]\\dfrac{17}{28}\\left(\\dfrac{\u00d72}{\u00d72}\\right)=\\dfrac{34}{56}[\/latex] so [latex]\\dfrac{49}{56}\u2265\\dfrac{34}{56}[\/latex]<\/p>\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>Change the fractions to have the same denominators. Decide which is larger. Use &gt; , &lt; , = to mark your answer. There is space below each problem to work out your equivalent fractions.<\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>[latex]\\dfrac{1}{4}[\/latex]<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> [latex]\\dfrac{3}{5}[\/latex]<\/li>\n<li>[latex]\\dfrac{5}{8}[\/latex]<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span>[latex]\\dfrac{3}{4}[\/latex]<\/li>\n<li>[latex]\\dfrac{1}{5}[\/latex]<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> [latex]\\dfrac{2}{3}[\/latex]<\/li>\n<li>[latex]\\dfrac{2}{3}[\/latex]<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> [latex]\\dfrac{3}{4}[\/latex]<\/li>\n<li>[latex]\\dfrac{49}{56}[\/latex] <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> [latex]\\dfrac{3}{4}[\/latex]<\/li>\n<li>[latex]\\dfrac{75}{90}[\/latex] <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> [latex]\\dfrac{10}{11}[\/latex]<\/li>\n<li>[latex]\\dfrac{33}{70}[\/latex] <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> [latex]\\dfrac{1}{2}[\/latex]<\/li>\n<li>[latex]\\dfrac{1}{3}[\/latex] <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>[latex]\\dfrac{1}{9}[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise One<\/strong><\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>&lt;<\/li>\n<li>&lt;<\/li>\n<li>&lt;<\/li>\n<li>&lt;<\/li>\n<li>&gt;<\/li>\n<li>&lt;<\/li>\n<li>&lt;<\/li>\n<li>&gt;<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1>Comparing Fractions to Decimals and Decimals to Fractions<\/h1>\n<p>Now that you know how to convert between fractions and decimals, you are also going to be able to compare them.<\/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>Which is larger: [latex]\\dfrac{3}{8}[\/latex] or 0.125?<\/p>\n<ol>\n<li>Decide to convert either the fraction into a decimal, or the decimal into a fraction. Let\u2019s pick converting the fraction into a decimal.<\/li>\n<li>Do the conversion[latex]\\dfrac{3}{8}[\/latex] =[latex]\\begin{array}{r}0.375\\\\ 8\\enclose{longdiv}{3.000}\\\\ 24\\downarrow \\ \\ \\\\ \\hline60\\hspace{0.8em}\\\\56\\downarrow\\\\\\hline40\\hspace{0.1em}\\\\40\\hspace{0.1em}\\\\\\hline\\end{array}[\/latex]\u00a0 \u00a0 \u00a0= 0.375<\/li>\n<li>Compare\u00a0<span class=\"ui-provider ank b c d e f g h i j k l m n o p q r s t u v w x y z ab ac ae af ag ah ai aj ak\" dir=\"ltr\">[latex]0.375\\underline{\\hspace{0.5em}>\\hspace{0.5em}}0.125[\/latex]<\/span><\/li>\n<li>Write a math sentence to show your answer: [latex]\\dfrac{3}{8}\\underline{\\hspace{0.5em}>\\hspace{0.5em}}0.125[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example B<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Which is larger[latex]\\dfrac{7}{8}[\/latex] or 0.6?<\/p>\n<ol>\n<li>Pick which you will convert, the decimal into the fraction, or the fraction into the decimal.\u00a0 <strong>Let\u2019s pick converting the decimal this time.<\/strong><\/li>\n<li>Convert 0.6= [latex]\\dfrac{6}{10}\\left(\\dfrac{ \u00f7 2}{ \u00f7 2}\\right) = \\dfrac{3}{5}[\/latex]<\/li>\n<li>Compare [latex]\\dfrac{7}{8}[\/latex] to [latex]\\dfrac{3}{5}[\/latex][latex]\\longrightarrow\\dfrac{7}{8}\\left(\\dfrac{ \u00d7 5}{ \u00d7 5}\\right) = \\dfrac{35}{40}[\/latex] ; [latex]\\dfrac{3}{5}\\left(\\dfrac{ \u00d7 8}{ \u00d7 8}\\right) = \\dfrac{24}{40}[\/latex]<\/li>\n<li>Write a math sentence to show your answer [latex]\\dfrac{7}{8}\\underline{\\hspace{0.5em} >\\hspace{0.5em}}0.6[\/latex]<\/li>\n<\/ol>\n<p>TIP: You may find that converting the fractions to the decimals could speed things up.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Compare<\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>0.25 <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>[latex]\\dfrac{1}{5}[\/latex]<\/li>\n<li>[latex]\\dfrac{1}{8}[\/latex]<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>\u00a00.8<\/li>\n<li>[latex]\\dfrac{1}{6}[\/latex]<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>\u00a0 0.125<\/li>\n<li>0.2<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>[latex]\\dfrac{3}{10}[\/latex]<\/li>\n<li>0.3725<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>[latex]\\dfrac{2}{3}[\/latex]<\/li>\n<li>[latex]\\dfrac{2}{5}[\/latex]<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>0.5<\/li>\n<li>0.3725<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>[latex]\\dfrac{1}{5}[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise Two<\/strong><\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>&gt;<\/li>\n<li>&lt;<\/li>\n<li>&gt;<\/li>\n<li>&lt;<\/li>\n<li>&lt;<\/li>\n<li>&lt;<\/li>\n<li>&gt;<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><strong>Compare the following numbers to each other. Use &gt; or &lt; .<\/strong><\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>0.345<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>[latex]\\dfrac{6}{7}[\/latex]<\/li>\n<li>[latex]\\dfrac{1}{1051}[\/latex]<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>0.0032<\/li>\n<li>0.52<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>[latex]\\dfrac{2}{3}[\/latex]<\/li>\n<li>0.6894<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>[latex]\\dfrac{103}{278}[\/latex]<\/li>\n<li>[latex]\\dfrac{1}{72}[\/latex]<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>[latex]\\dfrac{2}{3}[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise Three<\/strong><\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>&lt;<\/li>\n<li>&lt;<\/li>\n<li>&lt;<\/li>\n<li>&gt;<\/li>\n<li>&lt;<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1>Topic B Self-Test<\/h1>\n<p><strong>Mark \/18\u00a0 Aim 15 \/ 18<\/strong><\/p>\n<ol type=\"A\">\n<li>Write as common fractions in lowest terms. (4 marks)\n<ol class=\"twocolumn\" type=\"a\">\n<li>3.6<\/li>\n<li>8.125<\/li>\n<li>0.75<\/li>\n<li>0.45<\/li>\n<\/ol>\n<\/li>\n<li>Write as decimals. Round your answers to 3 decimal places. (4 marks)\n<ol class=\"twocolumn\" type=\"a\">\n<li>[latex]\\dfrac{3}{5}[\/latex]<\/li>\n<li>[latex]\\dfrac{6}{100}[\/latex]<\/li>\n<li>[latex]\\dfrac{3}{8}[\/latex]<\/li>\n<li>[latex]\\dfrac{5}{7}[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>Compare the following fractions and decimals, use &lt; , or &gt;. (6 marks)\n<ol class=\"twocolumn space\" type=\"a\">\n<li>0.862 <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> [latex]\\dfrac{6}{7}[\/latex]<\/li>\n<li>[latex]\\dfrac{3}{14}[\/latex] <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> 0.35<\/li>\n<li>[latex]\\dfrac{1}{10}[\/latex] <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> \u00a0 0.007<\/li>\n<li>0.3<span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>[latex]\\dfrac{20}{26}[\/latex]<\/li>\n<li>0.5 <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> [latex]\\dfrac{10}{21}[\/latex]<\/li>\n<li>[latex]\\dfrac{89}{90}[\/latex]\u00a0 <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> 0.473<\/li>\n<li>[latex]\\dfrac{1}{3}[\/latex]\u00a0 <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>[latex]\\dfrac{1}{9}[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>Problems. 4 marks\n<ol type=\"a\">\n<li>May babysat for [latex]4 \\tfrac{1}{4}[\/latex] hours. She is paid $4.75 an hour. How much did she earn?<\/li>\n<li>Diane bought 1.5 litres of milk. Her thirsty kids drank half of it as soon as she got home. How much milk is left?<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<h1>Answers to Topic B Self-Test<\/h1>\n<ol type=\"A\">\n<li>\n<ol class=\"twocolumn\" type=\"a\">\n<li>[latex]3\\dfrac{3}{5}[\/latex]<\/li>\n<li>[latex]8\\dfrac{1}{8}[\/latex]<\/li>\n<li>[latex]\\dfrac{3}{4}[\/latex]<\/li>\n<li>[latex]\\dfrac{9}{20}[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol class=\"twocolumn\" type=\"a\">\n<li>0.6<\/li>\n<li>0.06<\/li>\n<li>0.375<\/li>\n<li>0.714<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol class=\"twocolumn\" type=\"a\">\n<li>&gt;<\/li>\n<li>&lt;<\/li>\n<li>&gt;<\/li>\n<li>&lt;<\/li>\n<li>&gt;<\/li>\n<li>&gt;<\/li>\n<li>&gt;<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol class=\"twocolumn\" type=\"a\">\n<li>$20.19<\/li>\n<li>0.75 L<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n","protected":false},"author":999,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-203","chapter","type-chapter","status-publish","hentry"],"part":200,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/math025\/wp-json\/pressbooks\/v2\/chapters\/203","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/math025\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/math025\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math025\/wp-json\/wp\/v2\/users\/999"}],"version-history":[{"count":4,"href":"https:\/\/pressbooks.bccampus.ca\/math025\/wp-json\/pressbooks\/v2\/chapters\/203\/revisions"}],"predecessor-version":[{"id":391,"href":"https:\/\/pressbooks.bccampus.ca\/math025\/wp-json\/pressbooks\/v2\/chapters\/203\/revisions\/391"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/math025\/wp-json\/pressbooks\/v2\/parts\/200"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/math025\/wp-json\/pressbooks\/v2\/chapters\/203\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/math025\/wp-json\/wp\/v2\/media?parent=203"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math025\/wp-json\/pressbooks\/v2\/chapter-type?post=203"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math025\/wp-json\/wp\/v2\/contributor?post=203"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math025\/wp-json\/wp\/v2\/license?post=203"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}