{"id":10360,"date":"2017-05-26T18:47:14","date_gmt":"2017-05-26T18:47:14","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=10360"},"modified":"2024-04-30T16:34:04","modified_gmt":"2024-04-30T16:34:04","slug":"converting-fractions-to-decimals","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/converting-fractions-to-decimals\/","title":{"raw":"Converting Fractions to Decimals","rendered":"Converting Fractions to Decimals"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Convert fractions to decimals<\/li>\r\n \t<li>Identify a fraction whose decimal form is repeating<\/li>\r\n \t<li>Add a fraction and a decimal by converting between forms<\/li>\r\n<\/ul>\r\n<\/div>\r\nWe know how to convert decimals to fractions and 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.\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\n&nbsp;\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&nbsp;\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 Solution[\/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&nbsp;\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\n<h2 data-type=\"title\">Repeating Decimals<\/h2>\r\nSo far, in all the examples converting fractions to decimals the division resulted in a remainder of zero. This is not always the case. Let\u2019s see what happens when we convert the fraction [latex]{\\Large\\frac{4}{3}}[\/latex] to a decimal. First, notice that [latex]{\\Large\\frac{4}{3}}[\/latex] is an improper fraction. Its value is greater than [latex]1[\/latex]. The equivalent decimal will also be greater than [latex]1[\/latex].\r\n<p style=\"text-align: center;\">We divide [latex]4[\/latex] by [latex]3[\/latex].<\/p>\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221632\/CNX_BMath_Figure_05_03_004_img.png\" alt=\"A division problem is shown. 4.000 is on the inside of the division sign and 3 is on the outside. Below the 4 is a 3 with a line below it. Below the line is a 10. Below the 10 is a 9 with a line below it. Below the line is another 10, followed by another 9 with a line, followed by another 10, followed by another 9 with a line, followed by a 1. Above the division sign is 1.333...\" data-media-type=\"image\/png\" \/>\r\nNo matter how many more zeros we write, there will always be a remainder of [latex]1[\/latex], and the threes in the quotient will go on forever. The number [latex]\\text{1.333}\\dots [\/latex] is called a repeating decimal. Remember that the \"\u2026\" means that the pattern repeats.\r\n<div class=\"textbox shaded\">\r\n<h3>Repeating Decimal<\/h3>\r\nA repeating decimal is a decimal in which the last digit or group of digits repeats endlessly.\r\n\r\n<\/div>\r\nHow do you know how many \u2018repeats\u2019 to write? Instead of writing [latex]1.333\\dots [\/latex] we use a shorthand notation by placing a line over the digits that repeat. The repeating decimal [latex]1.333\\dots [\/latex] is written [latex]1.\\overline{3}[\/latex]. The line above the [latex]3[\/latex] tells you that the [latex]3[\/latex] repeats endlessly. So [latex]\\text{1.333}\\dots=1.\\overline{3}[\/latex]\r\n\r\nFor other decimals, two or more digits might repeat. The table below\u00a0shows some more examples of repeating decimals.\r\n<table id=\"fs-id2266631\" summary=\"A table with four rows and two columns. In the first column of the first row is 1.333... is equal to 1.3 with a bar above the 3. In the second column of the first row is the text \">\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">[latex]\\text{1.333}\\ldots=1.\\overline{3}[\/latex]<\/td>\r\n<td data-align=\"left\">[latex]3[\/latex] is the repeating digit<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">[latex]\\text{4.1666}\\ldots=4.1\\overline{6}[\/latex]<\/td>\r\n<td>[latex]6[\/latex] is the repeating digit<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">[latex]\\text{4.161616}\\ldots=4.\\overline{16}[\/latex]<\/td>\r\n<td data-align=\"left\">[latex]16[\/latex] is the repeating block<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">[latex]\\text{0.271271271}\\ldots =0.\\overline{271}[\/latex]<\/td>\r\n<td data-align=\"left\">[latex]271[\/latex] is the repeating block<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nWrite [latex]{\\Large\\frac{43}{22}}[\/latex] as a decimal.\r\n[reveal-answer q=\"496064\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"496064\"]\r\n\r\nSolution\r\nDivide [latex]43[\/latex] by [latex]22[\/latex]\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221633\/CNX_BMath_Figure_05_03_005_img.png\" alt=\"A division problem is shown. 43.00000 is on the inside of the division sign and 22 is on the outside. Below the 43 is a 22 with a line below it. Below the line is a 210 with a 198 with a line below it. Below the line is a 120 with 110 and a line below it. Below the line is 100 with 88 and a line below it. Below the line is 120 with 110 and a line below it. Below the line is 100 with 88 and a line below it. Below the line is an ellipses. There are arrows pointing to the 120s saying 120 repeats. There are arrows pointing to the 100s saying 100 repeats. There are arrows pointing to the patterns, in red, \u201cThe pattern repeats, so the numbers in the quotient will repeat as well.\u201d The quotient is shown above the division sign. It is 1.95454.\" width=\"485\" height=\"269\" data-media-type=\"image\/png\" \/>\r\nNotice that the differences of [latex]120[\/latex] and [latex]100[\/latex] repeat, so there is a repeat in the digits of the quotient; [latex]54[\/latex] will repeat endlessly. The first decimal place in the quotient, [latex]9[\/latex], is not part of the pattern. So,\r\n\r\n[latex]{\\Large\\frac{43}{22}}=1.9\\overline{54}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146259[\/ohm_question]\r\n\r\n<\/div>\r\nThe next video example shows an example of converting fractions to decimals when the result is repeating.\r\n\r\nhttps:\/\/youtu.be\/UHQrykNrlOM\r\n\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 Solution[\/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=\"7.000 divided by 8 equals 0.875. 8 goes into 70 8 times remainder 6. Carry the 0, 8 goes into 60 7 times remainder 4. Carry the 0, 8 goes into 40 5 times remainder 0.\" 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&nbsp;\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 Outcomes<\/h3>\n<ul>\n<li>Convert fractions to decimals<\/li>\n<li>Identify a fraction whose decimal form is repeating<\/li>\n<li>Add a fraction and a decimal by converting between forms<\/li>\n<\/ul>\n<\/div>\n<p>We know how to convert decimals to fractions and 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>&nbsp;<\/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<p>&nbsp;<\/p>\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-1\" 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 Solution<\/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<p>&nbsp;<\/p>\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<h2 data-type=\"title\">Repeating Decimals<\/h2>\n<p>So far, in all the examples converting fractions to decimals the division resulted in a remainder of zero. This is not always the case. Let\u2019s see what happens when we convert the fraction [latex]{\\Large\\frac{4}{3}}[\/latex] to a decimal. First, notice that [latex]{\\Large\\frac{4}{3}}[\/latex] is an improper fraction. Its value is greater than [latex]1[\/latex]. The equivalent decimal will also be greater than [latex]1[\/latex].<\/p>\n<p style=\"text-align: center;\">We divide [latex]4[\/latex] by [latex]3[\/latex].<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221632\/CNX_BMath_Figure_05_03_004_img.png\" alt=\"A division problem is shown. 4.000 is on the inside of the division sign and 3 is on the outside. Below the 4 is a 3 with a line below it. Below the line is a 10. Below the 10 is a 9 with a line below it. Below the line is another 10, followed by another 9 with a line, followed by another 10, followed by another 9 with a line, followed by a 1. Above the division sign is 1.333...\" data-media-type=\"image\/png\" \/><br \/>\nNo matter how many more zeros we write, there will always be a remainder of [latex]1[\/latex], and the threes in the quotient will go on forever. The number [latex]\\text{1.333}\\dots[\/latex] is called a repeating decimal. Remember that the &#8220;\u2026&#8221; means that the pattern repeats.<\/p>\n<div class=\"textbox shaded\">\n<h3>Repeating Decimal<\/h3>\n<p>A repeating decimal is a decimal in which the last digit or group of digits repeats endlessly.<\/p>\n<\/div>\n<p>How do you know how many \u2018repeats\u2019 to write? Instead of writing [latex]1.333\\dots[\/latex] we use a shorthand notation by placing a line over the digits that repeat. The repeating decimal [latex]1.333\\dots[\/latex] is written [latex]1.\\overline{3}[\/latex]. The line above the [latex]3[\/latex] tells you that the [latex]3[\/latex] repeats endlessly. So [latex]\\text{1.333}\\dots=1.\\overline{3}[\/latex]<\/p>\n<p>For other decimals, two or more digits might repeat. The table below\u00a0shows some more examples of repeating decimals.<\/p>\n<table id=\"fs-id2266631\" summary=\"A table with four rows and two columns. In the first column of the first row is 1.333... is equal to 1.3 with a bar above the 3. In the second column of the first row is the text\">\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"left\">[latex]\\text{1.333}\\ldots=1.\\overline{3}[\/latex]<\/td>\n<td data-align=\"left\">[latex]3[\/latex] is the repeating digit<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">[latex]\\text{4.1666}\\ldots=4.1\\overline{6}[\/latex]<\/td>\n<td>[latex]6[\/latex] is the repeating digit<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">[latex]\\text{4.161616}\\ldots=4.\\overline{16}[\/latex]<\/td>\n<td data-align=\"left\">[latex]16[\/latex] is the repeating block<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">[latex]\\text{0.271271271}\\ldots =0.\\overline{271}[\/latex]<\/td>\n<td data-align=\"left\">[latex]271[\/latex] is the repeating block<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Write [latex]{\\Large\\frac{43}{22}}[\/latex] as a decimal.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q496064\">Show Solution<\/span><\/p>\n<div id=\"q496064\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nDivide [latex]43[\/latex] by [latex]22[\/latex]<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221633\/CNX_BMath_Figure_05_03_005_img.png\" alt=\"A division problem is shown. 43.00000 is on the inside of the division sign and 22 is on the outside. Below the 43 is a 22 with a line below it. Below the line is a 210 with a 198 with a line below it. Below the line is a 120 with 110 and a line below it. Below the line is 100 with 88 and a line below it. Below the line is 120 with 110 and a line below it. Below the line is 100 with 88 and a line below it. Below the line is an ellipses. There are arrows pointing to the 120s saying 120 repeats. There are arrows pointing to the 100s saying 100 repeats. There are arrows pointing to the patterns, in red, \u201cThe pattern repeats, so the numbers in the quotient will repeat as well.\u201d The quotient is shown above the division sign. It is 1.95454.\" width=\"485\" height=\"269\" data-media-type=\"image\/png\" \/><br \/>\nNotice that the differences of [latex]120[\/latex] and [latex]100[\/latex] repeat, so there is a repeat in the digits of the quotient; [latex]54[\/latex] will repeat endlessly. The first decimal place in the quotient, [latex]9[\/latex], is not part of the pattern. So,<\/p>\n<p>[latex]{\\Large\\frac{43}{22}}=1.9\\overline{54}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146259\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146259&theme=oea&iframe_resize_id=ohm146259&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>The next video example shows an example of converting fractions to decimals when the result is repeating.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Ex 3:  Convert a Fraction to a Decimal (repeating)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/UHQrykNrlOM?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\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 Solution<\/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=\"7.000 divided by 8 equals 0.875. 8 goes into 70 8 times remainder 6. Carry the 0, 8 goes into 60 7 times remainder 4. Carry the 0, 8 goes into 40 5 times remainder 0.\" 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<p>&nbsp;<\/p>\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-10360\">\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 146263. 146261, 146259, 146257, 146253. <strong>Authored by<\/strong>: LumenLearning. <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 Fraction to a Decimal (terminating). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/P0IB7LfeaU4\">https:\/\/youtu.be\/P0IB7LfeaU4<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/pdm\">Public Domain: No Known Copyright<\/a><\/em><\/li><li>Ex 3: Convert a Fraction to a Decimal (repeating). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/UHQrykNrlOM\">https:\/\/youtu.be\/UHQrykNrlOM<\/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: 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":15,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"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\"},{\"type\":\"cc\",\"description\":\"Ex 1: Convert a Fraction to a Decimal (terminating)\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/P0IB7LfeaU4\",\"project\":\"\",\"license\":\"pd\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex 3: Convert a Fraction to a Decimal (repeating)\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/UHQrykNrlOM\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Question ID 146263. 146261, 146259, 146257, 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