{"id":327,"date":"2018-04-16T23:52:59","date_gmt":"2018-04-16T23:52:59","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/?post_type=chapter&#038;p=327"},"modified":"2024-04-26T22:02:57","modified_gmt":"2024-04-26T22:02:57","slug":"convert-between-decimals-and-fractions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/chapter\/convert-between-decimals-and-fractions\/","title":{"raw":"Convert Between Decimals and Fractions","rendered":"Convert Between Decimals and Fractions"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning OUTCOME<\/h3>\r\n<ul>\r\n \t<li>Convert decimals to fractions and fractions to decimals<\/li>\r\n<\/ul>\r\n<\/div>\r\n<p data-type=\"title\">We often need to rewrite decimals as fractions or mixed numbers. Let\u2019s go back to that 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>\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 to a fraction or mixed number<\/h3>\r\n<ol id=\"eip-id1168468271407\" class=\"stepwise\" data-number-style=\"arabic\">\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<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, \" data-label=\"\">\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 class=\"alignnone\" 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=\"4 written as the whole part of the mixed number. \" width=\"216\" height=\"57\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Determine the place value of the final digit.<\/td>\r\n<td><img class=\"alignnone\" 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=\"4.09. The 0 is labeled the tenths place, and the 9 is labeled the hundredths place.\" width=\"216\" height=\"41\" data-media-type=\"image\/png\" \/><\/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 class=\"alignnone\" 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=\"4 written as the whole part of the mixed number, and 9 written as the numerator to the fraction part of the mixed number.\" width=\"216\" height=\"45\" data-media-type=\"image\/png\" \/><\/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, \" data-label=\"\">\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 class=\"alignnone\" 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=\"3 written as the whole part of the mixed number.\" width=\"118\" height=\"56\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Determine the place value of the final digit.<\/td>\r\n<td><img class=\"alignnone\" 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=\"3.7. 7 is labeled the tenths place.\" width=\"118\" height=\"42\" data-media-type=\"image\/png\" \/><\/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 class=\"alignnone\" 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=\"3 written as the whole part of the mixed number, and 7 written as the numerator to the fraction part of the mixed number.\" width=\"117\" height=\"44\" data-media-type=\"image\/png\" \/><\/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, \" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>3.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]-0.286[\/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 class=\"alignnone\" 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=\"a negative sign preceding the fraction\" width=\"284\" height=\"53\" data-media-type=\"image\/png\" \/><\/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 class=\"alignnone\" 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=\"negative 0.286. 2 is labeled the tenths place, 8 is labeled the hundredths palce, and 6 is labeleed the thousandths place.\" width=\"284\" height=\"43\" data-media-type=\"image\/png\" \/><\/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<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\n<p data-type=\"title\">In the next video example, we who how to convert a decimal into a fraction.<\/p>\r\nhttps:\/\/youtu.be\/0yYQLZcTEXc\r\n\r\nNow we will do the reverse\u2014convert fractions to decimals. Remember that the fraction bar indicates division. So [latex]{\\Large\\frac{4}{5}}[\/latex] can be written [latex]4\\div 5[\/latex] or [latex]5\\overline{)4}[\/latex]. This means that we can convert a fraction to a decimal by treating it as a division problem.\r\n<div class=\"textbox shaded\">\r\n<h3>Convert a Fraction to a Decimal<\/h3>\r\nTo convert a fraction to a decimal, divide the numerator of the fraction by the denominator of the fraction.\r\n\r\n<\/div>\r\nThe next decimal shows how to dived a numerator by a denominator using long division, but you can always use a calculator if it's allowed in your class.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nWrite the fraction [latex]{\\Large\\frac{3}{4}}[\/latex] as a decimal.\r\n\r\nSolution\r\n<table id=\"eip-323\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>A fraction bar means division, so we can write the fraction [latex]\\Large\\frac{3}{4}[\/latex] using division.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221630\/CNX_BMath_Figure_05_03_001_img.png\" alt=\"A division problem is shown. 3 is on the inside of the division sign and 4 is on the outside.\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221630\/CNX_BMath_Figure_05_03_002_img.png\" alt=\"A division problem is shown. 3.00 is on the inside of the division sign and 4 is on the outside. Below the 3.00 is a 28 with a line below it. Below the line is a 20. Below the 20 is another 20 with a line below it. Below the line is a 0. Above the division sign is 0.75.\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>So the fraction [latex]{\\Large\\frac{3}{4}}[\/latex] is equal to [latex]0.75[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146253[\/ohm_question]\r\n\r\n<\/div>\r\nThe following video contains an example of how to write a fraction as a decimal.\r\n\r\nhttps:\/\/youtu.be\/P0IB7LfeaU4\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nWrite the fraction [latex]-{\\Large\\frac{7}{2}}[\/latex] as a decimal.\r\n[reveal-answer q=\"746734\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"746734\"]\r\n\r\nSolution\r\n<table id=\"eip-46\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>The value of this fraction is negative. After dividing, the value of the decimal will be negative. We do the division ignoring the sign, and then write the negative sign in the answer.<\/td>\r\n<td>[latex]-{\\Large\\frac{7}{2}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide [latex]7[\/latex] by [latex]2[\/latex]<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221631\/CNX_BMath_Figure_05_03_003_img.png\" alt=\"A division problem is shown. 7.0 is on the inside of the division sign and 2 is on the outside. Below the 7 is a 6 with a line below it. Below the line is a 10. Below the 10 is another 10 with a line below it. Below the line is a 0. 3.5 is written above the division sign.\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>\u00a0So,<\/td>\r\n<td>[latex]-{\\Large\\frac{7}{2}}=-3.5[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146257[\/ohm_question]\r\n\r\n<\/div>\r\nIt is useful to convert between fractions and decimals when we need to add or subtract numbers in different forms. To add a fraction and a decimal, for example, we would need to either convert the fraction to a decimal or the decimal to a fraction.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify: [latex]{\\Large\\frac{7}{8}}+6.4[\/latex]\r\n[reveal-answer q=\"422720\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"422720\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168575382181\" class=\"unnumbered unstyled\" summary=\"The problem says 7 over 8 plus 6.4. The first step says to change 7 over 8 to a decimal. It shows 7.000 being divided by 8. Below the 7.0 is a 64 with a line. Below the line is a 60. Below the 60 is a 56 with a line, followed by a 40. Below the 40 is another 40 with a line, followed by a 0. 0.875 is shown above the division sign. The next step says to add and shows 0.875 plus 6.4. The solution is 7.275.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>[latex]{\\Large\\frac{7}{8}}+6.4[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Change [latex]\\frac{7}{8}[\/latex] to a decimal.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221635\/CNX_BMath_Figure_05_03_011_img-01.png\" alt=\"Long divison for 7.000 divided by 8. 8 goes into 70 8 times, so 8 becomes the tenths digit in the quotient. 70 minus 64 equals 6, which becomes 60 when the 0 is carried down. 8 goes into 60 7 times, so 7 becomes the hundredths digit in the quotient. 60 minus 56 equals 4, which becomes 40 when the 0 is carried down. 8 goes into 40 5 times, so 5 becomes the thousandths place in the quotient. 40 minus 40 equals 0, so the remainder is 0. In total. 7 divided by 8. equals 0.875.\" width=\"94\" height=\"161\" data-media-type=\"image\/png\" \/><\/td>\r\n<td>[latex]0.875+6.4[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td><\/td>\r\n<td>[latex]7.275[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146261[\/ohm_question]\r\n\r\n[ohm_question]146263[\/ohm_question]\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning OUTCOME<\/h3>\n<ul>\n<li>Convert decimals to fractions and fractions to decimals<\/li>\n<\/ul>\n<\/div>\n<p data-type=\"title\">We often need to rewrite decimals as fractions or mixed numbers. Let\u2019s go back to that 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 to a fraction or mixed number<\/h3>\n<ol id=\"eip-id1168468271407\" class=\"stepwise\" data-number-style=\"arabic\">\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<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,\" data-label=\"\">\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 loading=\"lazy\" decoding=\"async\" class=\"alignnone\" 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=\"4 written as the whole part of the mixed number.\" width=\"216\" height=\"57\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td>Determine the place value of the final digit.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" 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=\"4.09. The 0 is labeled the tenths place, and the 9 is labeled the hundredths place.\" width=\"216\" height=\"41\" data-media-type=\"image\/png\" \/><\/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 loading=\"lazy\" decoding=\"async\" class=\"alignnone\" 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=\"4 written as the whole part of the mixed number, and 9 written as the numerator to the fraction part of the mixed number.\" width=\"216\" height=\"45\" data-media-type=\"image\/png\" \/><\/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,\" data-label=\"\">\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 loading=\"lazy\" decoding=\"async\" class=\"alignnone\" 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=\"3 written as the whole part of the mixed number.\" width=\"118\" height=\"56\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td>Determine the place value of the final digit.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" 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=\"3.7. 7 is labeled the tenths place.\" width=\"118\" height=\"42\" data-media-type=\"image\/png\" \/><\/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 loading=\"lazy\" decoding=\"async\" class=\"alignnone\" 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=\"3 written as the whole part of the mixed number, and 7 written as the numerator to the fraction part of the mixed number.\" width=\"117\" height=\"44\" data-media-type=\"image\/png\" \/><\/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,\" data-label=\"\">\n<tbody>\n<tr>\n<td>3.<\/td>\n<\/tr>\n<tr>\n<td>[latex]-0.286[\/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 loading=\"lazy\" decoding=\"async\" class=\"alignnone\" 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=\"a negative sign preceding the fraction\" width=\"284\" height=\"53\" data-media-type=\"image\/png\" \/><\/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 loading=\"lazy\" decoding=\"async\" class=\"alignnone\" 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=\"negative 0.286. 2 is labeled the tenths place, 8 is labeled the hundredths palce, and 6 is labeleed the thousandths place.\" width=\"284\" height=\"43\" data-media-type=\"image\/png\" \/><\/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<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 data-type=\"title\">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<p>Now we will do the reverse\u2014convert fractions to decimals. Remember that the fraction bar indicates division. So [latex]{\\Large\\frac{4}{5}}[\/latex] can be written [latex]4\\div 5[\/latex] or [latex]5\\overline{)4}[\/latex]. This means that we can convert a fraction to a decimal by treating it as a division problem.<\/p>\n<div class=\"textbox shaded\">\n<h3>Convert a Fraction to a Decimal<\/h3>\n<p>To convert a fraction to a decimal, divide the numerator of the fraction by the denominator of the fraction.<\/p>\n<\/div>\n<p>The next decimal shows how to dived a numerator by a denominator using long division, but you can always use a calculator if it&#8217;s allowed in your class.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Write the fraction [latex]{\\Large\\frac{3}{4}}[\/latex] as a decimal.<\/p>\n<p>Solution<\/p>\n<table id=\"eip-323\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>A fraction bar means division, so we can write the fraction [latex]\\Large\\frac{3}{4}[\/latex] using division.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221630\/CNX_BMath_Figure_05_03_001_img.png\" alt=\"A division problem is shown. 3 is on the inside of the division sign and 4 is on the outside.\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td>Divide.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221630\/CNX_BMath_Figure_05_03_002_img.png\" alt=\"A division problem is shown. 3.00 is on the inside of the division sign and 4 is on the outside. Below the 3.00 is a 28 with a line below it. Below the line is a 20. Below the 20 is another 20 with a line below it. Below the line is a 0. Above the division sign is 0.75.\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>So the fraction [latex]{\\Large\\frac{3}{4}}[\/latex] is equal to [latex]0.75[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146253\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146253&theme=oea&iframe_resize_id=ohm146253&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>The following video contains an example of how to write a fraction as a decimal.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Ex 1:  Convert a Fraction to a Decimal (terminating)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/P0IB7LfeaU4?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Write the fraction [latex]-{\\Large\\frac{7}{2}}[\/latex] as a decimal.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q746734\">Show Answer<\/span><\/p>\n<div id=\"q746734\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-46\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>The value of this fraction is negative. After dividing, the value of the decimal will be negative. We do the division ignoring the sign, and then write the negative sign in the answer.<\/td>\n<td>[latex]-{\\Large\\frac{7}{2}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide [latex]7[\/latex] by [latex]2[\/latex]<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221631\/CNX_BMath_Figure_05_03_003_img.png\" alt=\"A division problem is shown. 7.0 is on the inside of the division sign and 2 is on the outside. Below the 7 is a 6 with a line below it. Below the line is a 10. Below the 10 is another 10 with a line below it. Below the line is a 0. 3.5 is written above the division sign.\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td>\u00a0So,<\/td>\n<td>[latex]-{\\Large\\frac{7}{2}}=-3.5[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146257\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146257&theme=oea&iframe_resize_id=ohm146257&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>It is useful to convert between fractions and decimals when we need to add or subtract numbers in different forms. To add a fraction and a decimal, for example, we would need to either convert the fraction to a decimal or the decimal to a fraction.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Simplify: [latex]{\\Large\\frac{7}{8}}+6.4[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q422720\">Show Answer<\/span><\/p>\n<div id=\"q422720\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168575382181\" class=\"unnumbered unstyled\" summary=\"The problem says 7 over 8 plus 6.4. The first step says to change 7 over 8 to a decimal. It shows 7.000 being divided by 8. Below the 7.0 is a 64 with a line. Below the line is a 60. Below the 60 is a 56 with a line, followed by a 40. Below the 40 is another 40 with a line, followed by a 0. 0.875 is shown above the division sign. The next step says to add and shows 0.875 plus 6.4. The solution is 7.275.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>[latex]{\\Large\\frac{7}{8}}+6.4[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Change [latex]\\frac{7}{8}[\/latex] to a decimal.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221635\/CNX_BMath_Figure_05_03_011_img-01.png\" alt=\"Long divison for 7.000 divided by 8. 8 goes into 70 8 times, so 8 becomes the tenths digit in the quotient. 70 minus 64 equals 6, which becomes 60 when the 0 is carried down. 8 goes into 60 7 times, so 7 becomes the hundredths digit in the quotient. 60 minus 56 equals 4, which becomes 40 when the 0 is carried down. 8 goes into 40 5 times, so 5 becomes the thousandths place in the quotient. 40 minus 40 equals 0, so the remainder is 0. In total. 7 divided by 8. equals 0.875.\" width=\"94\" height=\"161\" data-media-type=\"image\/png\" \/><\/td>\n<td>[latex]0.875+6.4[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td><\/td>\n<td>[latex]7.275[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146261\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146261&theme=oea&iframe_resize_id=ohm146261&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146263\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146263&theme=oea&iframe_resize_id=ohm146263&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\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-327\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/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: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":14,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"}]","CANDELA_OUTCOMES_GUID":"01e6499a-37ac-4c1c-b810-3012ec1008d9, 998c2f1d-b320-41b0-b8db-e9968c44eee8","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-327","chapter","type-chapter","status-publish","hentry"],"part":22,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters\/327","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":12,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters\/327\/revisions"}],"predecessor-version":[{"id":3987,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters\/327\/revisions\/3987"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/parts\/22"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters\/327\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/media?parent=327"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapter-type?post=327"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/contributor?post=327"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/license?post=327"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}