{"id":4090,"date":"2020-04-05T21:02:05","date_gmt":"2020-04-05T21:02:05","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=4090"},"modified":"2020-04-05T21:18:12","modified_gmt":"2020-04-05T21:18:12","slug":"writing-fractions-and-decimals-as-percents","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/chapter\/writing-fractions-and-decimals-as-percents\/","title":{"raw":"Writing Decimals and Fractions as Percents","rendered":"Writing Decimals and Fractions as Percents"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Convert a decimal to a percent<\/li>\r\n \t<li>Convert a fraction to a percent<\/li>\r\n<\/ul>\r\n<\/div>\r\nTo convert a decimal to a percent, remember that percent means per hundred. If we change the decimal to a fraction whose denominator is [latex]100[\/latex], it is easy to change that fraction to a percent.\r\n<div class=\"textbox shaded\">\r\n<h3>Convert a decimal to a percent.<\/h3>\r\n<ol id=\"eip-id1168469368569\" class=\"stepwise\">\r\n \t<li>Write the decimal as a fraction.<\/li>\r\n \t<li>If the denominator of the fraction is not [latex]100[\/latex], rewrite it as an equivalent fraction with denominator [latex]100[\/latex].<\/li>\r\n \t<li>Write this ratio as a percent.<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nConvert each decimal to a percent:\r\n\r\n1. [latex]0.05[\/latex]\r\n\r\n2.[latex]0.83[\/latex]\r\n\r\nSolution\r\n<table id=\"eip-id1168466164139\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]0.05[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a fraction. The denominator is [latex]100[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{5}{100}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write this ratio as a percent.<\/td>\r\n<td>[latex]5[\/latex]%<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168469757904\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]0.83[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The denominator is [latex]100[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{83}{100}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write this ratio as a percent.<\/td>\r\n<td>[latex]83[\/latex]%<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\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]146666[\/ohm_question]\r\n\r\n<\/div>\r\nTo convert a mixed number to a percent, we first write it as an improper fraction.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nConvert each decimal to a percent:\r\n1. [latex]1.05[\/latex]\r\n\r\n2. [latex]0.075[\/latex]\r\n[reveal-answer q=\"740440\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"740440\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468629696\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]0.05[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a fraction.<\/td>\r\n<td>[latex]1{\\Large\\frac{5}{100}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as an improper fraction. The denominator is [latex]100[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{105}{100}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write this ratio as a percent.<\/td>\r\n<td>[latex]105[\/latex]%<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nNotice that since [latex]1.05&gt;1[\/latex], the result is more than [latex]\\text{100%.}[\/latex]\r\n<table id=\"eip-id1168469711926\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]0.075[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a fraction. The denominator is [latex]1,000[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{75}{1,000}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide the numerator and denominator by [latex]10[\/latex], so that the denominator is [latex]100[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{7.5}{100}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write this ratio as a percent.<\/td>\r\n<td>[latex]7.5[\/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]146667[\/ohm_question]\r\n\r\n[ohm_question]146668[\/ohm_question]\r\n\r\n<\/div>\r\nLet's summarize the results from the previous examples in the table below\u00a0so we can look for a pattern.\r\n<table id=\"fs-id1166484082075\" summary=\"The table shows two columns and five rows. The first row is a header row and it labels each column \">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th>Decimal<\/th>\r\n<th>Percent<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>[latex]0.05[\/latex]<\/td>\r\n<td>[latex]\\text{5%}[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]0.83[\/latex]<\/td>\r\n<td>[latex]\\text{83%}[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]1.05[\/latex]<\/td>\r\n<td>[latex]\\text{105%}[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]0.075[\/latex]<\/td>\r\n<td>[latex]\\text{7.5%}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nDo you see the pattern? To convert a decimal to a percent, we move the decimal point two places to the right and then add the percent sign.\r\n\r\nThe next table uses the decimal numbers in the table above\u00a0and shows visually to convert them to percents by moving the decimal point two places to the right and then writing the [latex]%[\/latex] sign.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221859\/CNX_BMath_Figure_06_01_003.png\" alt=\"The figure shows two columns and five rows. The first row is a header row and it labels each column \" \/>\r\nIn an earlier lesson, we learned how to convert fractions to decimals. Now we also know how to change decimals to percents. So to convert a fraction to a percent, we first change it to a decimal and then convert that decimal to a percent.\r\n<div class=\"textbox shaded\">\r\n<h3>Convert a fraction to a percent<\/h3>\r\n<ol id=\"eip-id1168467345664\" class=\"stepwise\">\r\n \t<li>Convert the fraction to a decimal.<\/li>\r\n \t<li>Convert the decimal to a percent.<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nConvert each fraction or mixed number to a percent:\r\n\r\n1.\u00a0 [latex]{\\Large\\frac{3}{4}}[\/latex]\r\n\r\n2.\u00a0 [latex]{\\Large\\frac{11}{8}}[\/latex]\r\n\r\n3.\u00a0 [latex]2{\\Large\\frac{1}{5}}[\/latex]\r\n[reveal-answer q=\"32099\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"32099\"]\r\n\r\nSolution\r\nTo convert a fraction to a decimal, divide the numerator by the denominator.\r\n<table id=\"eip-id1168469639303\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to change the fraction, three-fourths, to a percent. It shows how the fraction is written as the decimal, 0.75, and then a percent by moving the decimal point two places to the right. The percent is 75%.\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<td>\u00a0[latex]{\\Large\\frac{3}{4}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Change to a decimal.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221904\/CNX_BMath_Figure_06_01_004_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a percent by moving the decimal two places.<\/td>\r\n<td>[latex]75[\/latex]%<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168467258997\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to change the improper fraction, eleven-fourths, to a percent. It shows how the fraction is written as the decimal, 1.375, and then a percent by moving the decimal point two places to the right. The percent is 137.5%.\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<td>\u00a0[latex]{\\Large\\frac{11}{8}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Change to a decimal.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221905\/CNX_BMath_Figure_06_01_005_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a percent by moving the decimal two places.<\/td>\r\n<td>[latex]137.5[\/latex]%<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168466275816\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to change the fraction, three-fourths, to a percent. It shows how the fraction is written as the decimal, 0.75, and then a percent by moving the decimal point two places to the right. The percent is 75%.\">\r\n<tbody>\r\n<tr>\r\n<td>3.<\/td>\r\n<td>\u00a0[latex]2{\\Large\\frac{1}{5}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as an improper fraction.<\/td>\r\n<td>[latex]{\\Large\\frac{11}{5}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Change to a decimal.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221905\/CNX_BMath_Figure_06_01_006_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a percent.<\/td>\r\n<td>[latex]220[\/latex]%<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\nConvert [latex]{\\Large\\frac{5}{7}}[\/latex] to a percent.\r\n[reveal-answer q=\"971702\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"971702\"]\r\n\r\nSolution\r\nTo change a fraction to a decimal, we divide the numerator by the denominator.\r\n<table id=\"eip-id1168469429567\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\Large\\frac{5}{7}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Change to a decimal\u2014rounding to the nearest thousandth.<\/td>\r\n<td>[latex]0.714[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a percent.<\/td>\r\n<td>[latex]71.4[\/latex]%<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nNotice that we needed to add zeros at the end of the number when moving the decimal two places to the right.\r\n\r\nSometimes when changing a fraction to a decimal, the division continues for many decimal places and we will round off the quotient. The number of decimal places we round to will depend on the situation. If the decimal involves money, we round to the hundredths place. For most other cases in this book we will round the number to the nearest thousandth, so the percent will be rounded to the nearest tenth.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146669[\/ohm_question]\r\n\r\n[ohm_question]146670[\/ohm_question]\r\n\r\n[ohm_question]146671[\/ohm_question]\r\n\r\n<\/div>\r\nTo summarize, here are the results from the previous example in a table.\r\n<table id=\"fs-id1166484082075\" summary=\"The table shows two columns and five rows. The first row is a header row and it labels each column \">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th>Fraction<\/th>\r\n<th>Decimal<\/th>\r\n<th>Percent<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\Large\\frac{3}{4}}[\/latex]<\/td>\r\n<td>[latex]0.75[\/latex]<\/td>\r\n<td>[latex]75[\/latex]%<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\Large\\frac{11}{8}}[\/latex]<\/td>\r\n<td>\u00a0[latex]1.375[\/latex]<\/td>\r\n<td>[latex]137.5[\/latex]%<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]2{\\Large\\frac{1}{5}} ={\\Large\\frac{11}{5}}[\/latex]<\/td>\r\n<td>\u00a0[latex]2.20[\/latex]<\/td>\r\n<td>[latex]220[\/latex]%<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<span style=\"color: #ff0000\">\u00a0<\/span>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Convert a decimal to a percent<\/li>\n<li>Convert a fraction to a percent<\/li>\n<\/ul>\n<\/div>\n<p>To convert a decimal to a percent, remember that percent means per hundred. If we change the decimal to a fraction whose denominator is [latex]100[\/latex], it is easy to change that fraction to a percent.<\/p>\n<div class=\"textbox shaded\">\n<h3>Convert a decimal to a percent.<\/h3>\n<ol id=\"eip-id1168469368569\" class=\"stepwise\">\n<li>Write the decimal as a fraction.<\/li>\n<li>If the denominator of the fraction is not [latex]100[\/latex], rewrite it as an equivalent fraction with denominator [latex]100[\/latex].<\/li>\n<li>Write this ratio as a percent.<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Convert each decimal to a percent:<\/p>\n<p>1. [latex]0.05[\/latex]<\/p>\n<p>2.[latex]0.83[\/latex]<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168466164139\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]0.05[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write as a fraction. The denominator is [latex]100[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{5}{100}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write this ratio as a percent.<\/td>\n<td>[latex]5[\/latex]%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168469757904\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]0.83[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>The denominator is [latex]100[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{83}{100}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write this ratio as a percent.<\/td>\n<td>[latex]83[\/latex]%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146666\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146666&theme=oea&iframe_resize_id=ohm146666&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>To convert a mixed number to a percent, we first write it as an improper fraction.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Convert each decimal to a percent:<br \/>\n1. [latex]1.05[\/latex]<\/p>\n<p>2. [latex]0.075[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q740440\">Show Solution<\/span><\/p>\n<div id=\"q740440\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468629696\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]0.05[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write as a fraction.<\/td>\n<td>[latex]1{\\Large\\frac{5}{100}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write as an improper fraction. The denominator is [latex]100[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{105}{100}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write this ratio as a percent.<\/td>\n<td>[latex]105[\/latex]%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Notice that since [latex]1.05>1[\/latex], the result is more than [latex]\\text{100%.}[\/latex]<\/p>\n<table id=\"eip-id1168469711926\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]0.075[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write as a fraction. The denominator is [latex]1,000[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{75}{1,000}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide the numerator and denominator by [latex]10[\/latex], so that the denominator is [latex]100[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{7.5}{100}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write this ratio as a percent.<\/td>\n<td>[latex]7.5[\/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=\"ohm146667\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146667&theme=oea&iframe_resize_id=ohm146667&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146668\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146668&theme=oea&iframe_resize_id=ohm146668&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Let&#8217;s summarize the results from the previous examples in the table below\u00a0so we can look for a pattern.<\/p>\n<table id=\"fs-id1166484082075\" summary=\"The table shows two columns and five rows. The first row is a header row and it labels each column\">\n<thead>\n<tr valign=\"top\">\n<th>Decimal<\/th>\n<th>Percent<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>[latex]0.05[\/latex]<\/td>\n<td>[latex]\\text{5%}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]0.83[\/latex]<\/td>\n<td>[latex]\\text{83%}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]1.05[\/latex]<\/td>\n<td>[latex]\\text{105%}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]0.075[\/latex]<\/td>\n<td>[latex]\\text{7.5%}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Do you see the pattern? To convert a decimal to a percent, we move the decimal point two places to the right and then add the percent sign.<\/p>\n<p>The next table uses the decimal numbers in the table above\u00a0and shows visually to convert them to percents by moving the decimal point two places to the right and then writing the [latex]%[\/latex] sign.<\/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\/24221859\/CNX_BMath_Figure_06_01_003.png\" alt=\"The figure shows two columns and five rows. The first row is a header row and it labels each column\" \/><br \/>\nIn an earlier lesson, we learned how to convert fractions to decimals. Now we also know how to change decimals to percents. So to convert a fraction to a percent, we first change it to a decimal and then convert that decimal to a percent.<\/p>\n<div class=\"textbox shaded\">\n<h3>Convert a fraction to a percent<\/h3>\n<ol id=\"eip-id1168467345664\" class=\"stepwise\">\n<li>Convert the fraction to a decimal.<\/li>\n<li>Convert the decimal to a percent.<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Convert each fraction or mixed number to a percent:<\/p>\n<p>1.\u00a0 [latex]{\\Large\\frac{3}{4}}[\/latex]<\/p>\n<p>2.\u00a0 [latex]{\\Large\\frac{11}{8}}[\/latex]<\/p>\n<p>3.\u00a0 [latex]2{\\Large\\frac{1}{5}}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q32099\">Show Solution<\/span><\/p>\n<div id=\"q32099\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nTo convert a fraction to a decimal, divide the numerator by the denominator.<\/p>\n<table id=\"eip-id1168469639303\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to change the fraction, three-fourths, to a percent. It shows how the fraction is written as the decimal, 0.75, and then a percent by moving the decimal point two places to the right. The percent is 75%.\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<td>\u00a0[latex]{\\Large\\frac{3}{4}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Change to a decimal.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221904\/CNX_BMath_Figure_06_01_004_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Write as a percent by moving the decimal two places.<\/td>\n<td>[latex]75[\/latex]%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168467258997\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to change the improper fraction, eleven-fourths, to a percent. It shows how the fraction is written as the decimal, 1.375, and then a percent by moving the decimal point two places to the right. The percent is 137.5%.\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<td>\u00a0[latex]{\\Large\\frac{11}{8}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Change to a decimal.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221905\/CNX_BMath_Figure_06_01_005_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Write as a percent by moving the decimal two places.<\/td>\n<td>[latex]137.5[\/latex]%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168466275816\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to change the fraction, three-fourths, to a percent. It shows how the fraction is written as the decimal, 0.75, and then a percent by moving the decimal point two places to the right. The percent is 75%.\">\n<tbody>\n<tr>\n<td>3.<\/td>\n<td>\u00a0[latex]2{\\Large\\frac{1}{5}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write as an improper fraction.<\/td>\n<td>[latex]{\\Large\\frac{11}{5}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Change to a decimal.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221905\/CNX_BMath_Figure_06_01_006_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Write as a percent.<\/td>\n<td>[latex]220[\/latex]%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<p>Convert [latex]{\\Large\\frac{5}{7}}[\/latex] to a percent.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q971702\">Show Solution<\/span><\/p>\n<div id=\"q971702\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nTo change a fraction to a decimal, we divide the numerator by the denominator.<\/p>\n<table id=\"eip-id1168469429567\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]\\Large\\frac{5}{7}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Change to a decimal\u2014rounding to the nearest thousandth.<\/td>\n<td>[latex]0.714[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write as a percent.<\/td>\n<td>[latex]71.4[\/latex]%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>Notice that we needed to add zeros at the end of the number when moving the decimal two places to the right.<\/p>\n<p>Sometimes when changing a fraction to a decimal, the division continues for many decimal places and we will round off the quotient. The number of decimal places we round to will depend on the situation. If the decimal involves money, we round to the hundredths place. For most other cases in this book we will round the number to the nearest thousandth, so the percent will be rounded to the nearest tenth.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146669\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146669&theme=oea&iframe_resize_id=ohm146669&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146670\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146670&theme=oea&iframe_resize_id=ohm146670&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146671\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146671&theme=oea&iframe_resize_id=ohm146671&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>To summarize, here are the results from the previous example in a table.<\/p>\n<table id=\"fs-id1166484082075\" summary=\"The table shows two columns and five rows. The first row is a header row and it labels each column\">\n<thead>\n<tr valign=\"top\">\n<th>Fraction<\/th>\n<th>Decimal<\/th>\n<th>Percent<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>[latex]{\\Large\\frac{3}{4}}[\/latex]<\/td>\n<td>[latex]0.75[\/latex]<\/td>\n<td>[latex]75[\/latex]%<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\Large\\frac{11}{8}}[\/latex]<\/td>\n<td>\u00a0[latex]1.375[\/latex]<\/td>\n<td>[latex]137.5[\/latex]%<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]2{\\Large\\frac{1}{5}} ={\\Large\\frac{11}{5}}[\/latex]<\/td>\n<td>\u00a0[latex]2.20[\/latex]<\/td>\n<td>[latex]220[\/latex]%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"color: #ff0000\">\u00a0<\/span><\/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-4090\">\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 146671, 146670, 146669, 146668, 146667. <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>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/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":25777,"menu_order":5,"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\":\"original\",\"description\":\"Question ID 146671, 146670, 146669, 146668, 146667\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + GPL\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-4090","chapter","type-chapter","status-publish","hentry"],"part":299,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4090","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/wp\/v2\/users\/25777"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4090\/revisions"}],"predecessor-version":[{"id":5439,"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4090\/revisions\/5439"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/parts\/299"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4090\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=4090"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=4090"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=4090"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=4090"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}