{"id":10342,"date":"2017-05-26T18:38:52","date_gmt":"2017-05-26T18:38:52","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=10342"},"modified":"2020-09-11T00:21:11","modified_gmt":"2020-09-11T00:21:11","slug":"converting-decimals-to-fractions-or-mixed-numbers","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/chapter\/converting-decimals-to-fractions-or-mixed-numbers\/","title":{"raw":"3.1.b - Converting Decimals to Fractions or Mixed Numbers","rendered":"3.1.b &#8211; Converting Decimals to Fractions or Mixed Numbers"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Convert decimals to fractions or mixed numbers<\/li>\r\n<\/ul>\r\n<\/div>\r\nWe often need to rewrite decimals as fractions or mixed numbers. Let\u2019s go back to our lunch order to see how we can convert decimal numbers to fractions. We know that [latex]$5.03[\/latex] means [latex]5[\/latex] dollars and [latex]3[\/latex] cents. Since there are [latex]100[\/latex] cents in one dollar, [latex]3[\/latex] cents means [latex]{\\Large\\frac{3}{100}}[\/latex] of a dollar, so [latex]0.03={\\Large\\frac{3}{100}}[\/latex].\r\n\r\nWe convert decimals to fractions by identifying the place value of the farthest right digit. In the decimal [latex]0.03[\/latex], the [latex]3[\/latex] is in the hundredths place, so [latex]100[\/latex] is the denominator of the fraction equivalent to [latex]0.03[\/latex].\r\n<p style=\"text-align: center\">[latex]0.03={\\Large\\frac{3}{100}}[\/latex]<\/p>\r\nFor our [latex]$5.03[\/latex] lunch, we can write the decimal [latex]5.03[\/latex] as a mixed number.\r\n<p style=\"text-align: center\">[latex]5.03=5{\\Large\\frac{3}{100}}[\/latex]<\/p>\r\nNotice that when the number to the left of the decimal is zero, we get a proper fraction. When the number to the left of the decimal is not zero, we get a mixed number.\r\n<div class=\"textbox shaded\">\r\n<h3>Convert a decimal number to a fraction or mixed number.<\/h3>\r\n<ol id=\"eip-id1168468271407\" class=\"stepwise\">\r\n \t<li>Look at the number to the left of the decimal.\r\n<ul id=\"eip-id1168468271412\">\r\n \t<li>If it is zero, the decimal converts to a proper fraction.<\/li>\r\n \t<li>If it is not zero, the decimal converts to a mixed number.\r\n<ul id=\"eip-id1168468449219\">\r\n \t<li>Write the whole number.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Determine the place value of the final digit.<\/li>\r\n \t<li>Write the fraction.\r\n<ul id=\"eip-id1168468484466\">\r\n \t<li>numerator\u2014the \u2018numbers\u2019 to the right of the decimal point<\/li>\r\n \t<li>denominator\u2014the place value corresponding to the final digit<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Simplify the fraction, if possible.<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nWrite each of the following decimal numbers as a fraction or a mixed number:\r\n<ol>\r\n \t<li>[latex]4.09[\/latex]<\/li>\r\n \t<li>[latex]3.7[\/latex]<\/li>\r\n \t<li>[latex]-0.286[\/latex]<\/li>\r\n<\/ol>\r\nSolution:\r\n<table id=\"eip-id1168466515055\" class=\"unnumbered unstyled\" summary=\"The first line shows 4.09. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]4.09[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>There is a [latex]4[\/latex] to the left of the decimal point.\r\n\r\nWrite \"[latex]4[\/latex]\" as the whole number part of the mixed number.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221437\/CNX_BMath_Figure_05_01_014_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Determine the place value of the final digit.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221438\/CNX_BMath_Figure_05_01_014_img-02.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the fraction.\r\n\r\nWrite [latex]9[\/latex] in the numerator as it is the number to the right of the decimal point.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221439\/CNX_BMath_Figure_05_01_014_img-03.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write [latex]100[\/latex] in the denominator as the place value of the final digit, [latex]9[\/latex], is hundredth.<\/td>\r\n<td>[latex]4{\\Large\\frac{9}{100}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The fraction is in simplest form.<\/td>\r\n<td>So, [latex]4.09=4{\\Large\\frac{9}{100}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nDid you notice that the number of zeros in the denominator is the same as the number of decimal places?\r\n<table id=\"eip-id1168468328458\" class=\"unnumbered unstyled\" summary=\"The first line shows 3.7. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]3.7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>There is a [latex]3[\/latex] to the left of the decimal point.\r\n\r\nWrite \"[latex]3[\/latex]\" as the whole number part of the mixed number.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221445\/CNX_BMath_Figure_05_01_015_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Determine the place value of the final digit.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221446\/CNX_BMath_Figure_05_01_015_img-02.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the fraction.\r\n\r\nWrite [latex]7[\/latex] in the numerator as it is the number to the right of the decimal point.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221447\/CNX_BMath_Figure_05_01_015_img-03.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write [latex]10[\/latex] in the denominator as the place value of the final digit, [latex]7[\/latex], is tenths.<\/td>\r\n<td>[latex]3{\\Large\\frac{7}{10}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The fraction is in simplest form.<\/td>\r\n<td>So, [latex]3.7=3{\\Large\\frac{7}{10}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168468662484\" class=\"unnumbered unstyled\" summary=\"The first line shows negative 0.286. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td>3.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]\u22120.286[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>There is a [latex]0[\/latex] to the left of the decimal point.\r\n\r\nWrite a negative sign before the fraction.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221450\/CNX_BMath_Figure_05_01_016_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Determine the place value of the final digit and write it in the denominator.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221451\/CNX_BMath_Figure_05_01_016_img-02.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the fraction.\r\n\r\nWrite [latex]286[\/latex] in the numerator as it is the number to the right of the decimal point.\r\n\r\nWrite [latex]1,000[\/latex] in the denominator as the place value of the final digit, [latex]6[\/latex], is thousandths.<\/td>\r\n<td>[latex]-{\\Large\\frac{286}{1000}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>We remove a common factor of [latex]2[\/latex] to simplify the fraction.<\/td>\r\n<td>[latex]-{\\Large\\frac{143}{500}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146573[\/ohm_question]\r\n\r\n[ohm_question]146574[\/ohm_question]\r\n\r\n[ohm_question]146575[\/ohm_question]\r\n\r\n<\/div>\r\nIn the next video example, we who how to convert a decimal into a fraction.\r\n\r\nhttps:\/\/youtu.be\/0yYQLZcTEXc","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Convert decimals to fractions or mixed numbers<\/li>\n<\/ul>\n<\/div>\n<p>We often need to rewrite decimals as fractions or mixed numbers. Let\u2019s go back to our lunch order to see how we can convert decimal numbers to fractions. We know that [latex]$5.03[\/latex] means [latex]5[\/latex] dollars and [latex]3[\/latex] cents. Since there are [latex]100[\/latex] cents in one dollar, [latex]3[\/latex] cents means [latex]{\\Large\\frac{3}{100}}[\/latex] of a dollar, so [latex]0.03={\\Large\\frac{3}{100}}[\/latex].<\/p>\n<p>We convert decimals to fractions by identifying the place value of the farthest right digit. In the decimal [latex]0.03[\/latex], the [latex]3[\/latex] is in the hundredths place, so [latex]100[\/latex] is the denominator of the fraction equivalent to [latex]0.03[\/latex].<\/p>\n<p style=\"text-align: center\">[latex]0.03={\\Large\\frac{3}{100}}[\/latex]<\/p>\n<p>For our [latex]$5.03[\/latex] lunch, we can write the decimal [latex]5.03[\/latex] as a mixed number.<\/p>\n<p style=\"text-align: center\">[latex]5.03=5{\\Large\\frac{3}{100}}[\/latex]<\/p>\n<p>Notice that when the number to the left of the decimal is zero, we get a proper fraction. When the number to the left of the decimal is not zero, we get a mixed number.<\/p>\n<div class=\"textbox shaded\">\n<h3>Convert a decimal number to a fraction or mixed number.<\/h3>\n<ol id=\"eip-id1168468271407\" class=\"stepwise\">\n<li>Look at the number to the left of the decimal.\n<ul id=\"eip-id1168468271412\">\n<li>If it is zero, the decimal converts to a proper fraction.<\/li>\n<li>If it is not zero, the decimal converts to a mixed number.\n<ul id=\"eip-id1168468449219\">\n<li>Write the whole number.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li>Determine the place value of the final digit.<\/li>\n<li>Write the fraction.\n<ul id=\"eip-id1168468484466\">\n<li>numerator\u2014the \u2018numbers\u2019 to the right of the decimal point<\/li>\n<li>denominator\u2014the place value corresponding to the final digit<\/li>\n<\/ul>\n<\/li>\n<li>Simplify the fraction, if possible.<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Write each of the following decimal numbers as a fraction or a mixed number:<\/p>\n<ol>\n<li>[latex]4.09[\/latex]<\/li>\n<li>[latex]3.7[\/latex]<\/li>\n<li>[latex]-0.286[\/latex]<\/li>\n<\/ol>\n<p>Solution:<\/p>\n<table id=\"eip-id1168466515055\" class=\"unnumbered unstyled\" summary=\"The first line shows 4.09. The next line says,\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<\/tr>\n<tr>\n<td>[latex]4.09[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>There is a [latex]4[\/latex] to the left of the decimal point.<\/p>\n<p>Write &#8220;[latex]4[\/latex]&#8221; as the whole number part of the mixed number.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221437\/CNX_BMath_Figure_05_01_014_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Determine the place value of the final digit.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221438\/CNX_BMath_Figure_05_01_014_img-02.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Write the fraction.<\/p>\n<p>Write [latex]9[\/latex] in the numerator as it is the number to the right of the decimal point.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221439\/CNX_BMath_Figure_05_01_014_img-03.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Write [latex]100[\/latex] in the denominator as the place value of the final digit, [latex]9[\/latex], is hundredth.<\/td>\n<td>[latex]4{\\Large\\frac{9}{100}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>The fraction is in simplest form.<\/td>\n<td>So, [latex]4.09=4{\\Large\\frac{9}{100}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Did you notice that the number of zeros in the denominator is the same as the number of decimal places?<\/p>\n<table id=\"eip-id1168468328458\" class=\"unnumbered unstyled\" summary=\"The first line shows 3.7. The next line says,\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<\/tr>\n<tr>\n<td>[latex]3.7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>There is a [latex]3[\/latex] to the left of the decimal point.<\/p>\n<p>Write &#8220;[latex]3[\/latex]&#8221; as the whole number part of the mixed number.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221445\/CNX_BMath_Figure_05_01_015_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Determine the place value of the final digit.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221446\/CNX_BMath_Figure_05_01_015_img-02.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Write the fraction.<\/p>\n<p>Write [latex]7[\/latex] in the numerator as it is the number to the right of the decimal point.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221447\/CNX_BMath_Figure_05_01_015_img-03.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Write [latex]10[\/latex] in the denominator as the place value of the final digit, [latex]7[\/latex], is tenths.<\/td>\n<td>[latex]3{\\Large\\frac{7}{10}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>The fraction is in simplest form.<\/td>\n<td>So, [latex]3.7=3{\\Large\\frac{7}{10}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468662484\" class=\"unnumbered unstyled\" summary=\"The first line shows negative 0.286. The next line says,\">\n<tbody>\n<tr>\n<td>3.<\/td>\n<\/tr>\n<tr>\n<td>[latex]\u22120.286[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>There is a [latex]0[\/latex] to the left of the decimal point.<\/p>\n<p>Write a negative sign before the fraction.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221450\/CNX_BMath_Figure_05_01_016_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Determine the place value of the final digit and write it in the denominator.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221451\/CNX_BMath_Figure_05_01_016_img-02.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Write the fraction.<\/p>\n<p>Write [latex]286[\/latex] in the numerator as it is the number to the right of the decimal point.<\/p>\n<p>Write [latex]1,000[\/latex] in the denominator as the place value of the final digit, [latex]6[\/latex], is thousandths.<\/td>\n<td>[latex]-{\\Large\\frac{286}{1000}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>We remove a common factor of [latex]2[\/latex] to simplify the fraction.<\/td>\n<td>[latex]-{\\Large\\frac{143}{500}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146573\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146573&theme=oea&iframe_resize_id=ohm146573&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146574\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146574&theme=oea&iframe_resize_id=ohm146574&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146575\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146575&theme=oea&iframe_resize_id=ohm146575&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the next video example, we who how to convert a decimal into a fraction.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex 1:  Convert a Decimal to a Fraction\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/0yYQLZcTEXc?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-10342\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Question ID 146574, 146575, 146576. <strong>Authored by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Ex 1: Convert a Decimal to a Fraction. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/0yYQLZcTEXc\">https:\/\/youtu.be\/0yYQLZcTEXc<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: 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