{"id":335,"date":"2018-04-17T00:10:21","date_gmt":"2018-04-17T00:10:21","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/?post_type=chapter&#038;p=335"},"modified":"2024-04-26T22:03:21","modified_gmt":"2024-04-26T22:03:21","slug":"writing-fractions-and-decimals-as-percents","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/chapter\/writing-fractions-and-decimals-as-percents\/","title":{"raw":"Writing Fractions and Decimals as Percents","rendered":"Writing Fractions and Decimals as Percents"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcome<\/h3>\r\n<ul>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Use percent to represent a given fraction or decimal&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:13185,&quot;3&quot;:[null,0],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;,&quot;16&quot;:10}\">Use percent to represent a given fraction or decimal<\/span><\/li>\r\n<\/ul>\r\n<\/div>\r\nHow many cents are in one dollar? There are [latex]100[\/latex] cents in a dollar. How many years are in a century? There are [latex]100[\/latex] years in a century. Does this give you a clue about what the word \"percent\" means? It is really two words, \"per cent,\" and means per one hundred. A percent is a ratio whose denominator is [latex]100[\/latex]. We use the percent symbol, [latex]\\%[\/latex], to show percent.\r\n<div class=\"textbox shaded\">\r\n<h3>Percent<\/h3>\r\n<p style=\"padding-left: 60px;\">A percent is a ratio whose denominator is [latex]100[\/latex].<\/p>\r\n<p style=\"padding-left: 60px;\">For example [latex]46\\%=\\Large\\frac{46}{100}[\/latex]<\/p>\r\n\r\n<\/div>\r\nAccording to data from the American Association of Community Colleges [latex]\\left(2015\\right)[\/latex], about [latex]\\text{57%}[\/latex] of community college students are female. This means [latex]57[\/latex] out of every [latex]100[\/latex] community college students are female, as the image below\u00a0<span style=\"font-size: 16px;\">shows. Out of the [latex]100[\/latex] squares on the grid, [latex]57[\/latex] are shaded, which we write as the ratio [latex]\\Large\\frac{57}{100}[\/latex].<\/span>\r\n\r\nAmong every [latex]100[\/latex] community college students, [latex]57[\/latex] are female.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221858\/CNX_BMath_Figure_06_01_001.png\" alt=\"The figure shows a hundred flat with 57 units shaded.\" data-media-type=\"image\/png\" \/>\r\nSimilarly, [latex]\\text{25%}[\/latex] means a ratio of [latex]\\Large\\frac{25}{100}\\normalsize ,\\text{3%}[\/latex] means a ratio of [latex]\\Large\\frac{3}{100}[\/latex] and [latex]\\text{100%}[\/latex] means a ratio of [latex]\\Large\\frac{100}{100}[\/latex]. In words, \"one hundred percent\" means the total [latex]\\text{100%}[\/latex] is [latex]\\Large\\frac{100}{100}[\/latex], and since [latex]\\Large\\frac{100}{100}\\normalsize =1[\/latex], we see that [latex]\\text{100%}[\/latex] means [latex]1[\/latex] whole.\r\n<p data-type=\"title\">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>\r\n\r\n<div class=\"textbox shaded\">\r\n<h3>Convert a decimal to a percent<\/h3>\r\n<ol id=\"eip-id1168469368569\" class=\"stepwise\" data-number-style=\"arabic\">\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<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=\".\" data-label=\"\">\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. Five hundredths - 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=\".\" data-label=\"\">\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>Write as a fraction. Eighty-three hundredths - 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<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146666[\/ohm_question]\r\n\r\n<\/div>\r\nLet's look at a few more examples of converting decimals to percents, but these aren't as straight forward!\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nConvert each decimal to a percent:\r\n1. [latex]0.2[\/latex]\r\n\r\n2. [latex]1.05[\/latex]\r\n\r\n2. [latex]0.075[\/latex]\r\n\r\n[reveal-answer q=\"740440\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"740440\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168469711926\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\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]0.2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a fraction. The denominator is [latex]10[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{2}{10}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the numerator and denominator by [latex]10[\/latex], so that the denominator is [latex]100[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{20}{100}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write this ratio as a percent.<\/td>\r\n<td>[latex]20\\%[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nNotice that you could also have written\u00a0[latex]0.2[\/latex] as\u00a0[latex]0.20[\/latex] and gotten to\u00a0[latex]{\\Large\\frac{20}{100}}[\/latex] without doing any calculations.\r\n<table id=\"eip-id1168468629696\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\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]0.05[\/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]100\\%.[\/latex]\r\n<table id=\"eip-id1168469711926\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>3.<\/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\nNotice that any decimal that has value beyond the hundredths place will have a decimal answer when converted to a percent.\r\n\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]146667[\/ohm_question]\r\n\r\n[ohm_question]156959[\/ohm_question]\r\n\r\n[ohm_question]156964[\/ohm_question]\r\n\r\n<\/div>\r\nLet's summarize some of 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 data-align=\"left\">Decimal<\/th>\r\n<th data-align=\"left\">Percent<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">[latex]0.05[\/latex]<\/td>\r\n<td data-align=\"left\">[latex]\\text{5%}[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">[latex]0.83[\/latex]<\/td>\r\n<td data-align=\"left\">[latex]\\text{83%}[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">[latex]0.2[\/latex]<\/td>\r\n<td data-align=\"left\">[latex]\\text{20%}[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">[latex]1.05[\/latex]<\/td>\r\n<td data-align=\"left\">[latex]\\text{105%}[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">[latex]0.075[\/latex]<\/td>\r\n<td data-align=\"left\">[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<table id=\"fs-id1166484082063\" style=\"height: 70px;\" summary=\"The table shows two columns and five rows. The first row is a header row and it labels each column. The first column is labeled percent, and the second is labeled decimal. The rows read as follows: 6 percent and 0.06, 78 percent and 0.78, 135 percent and 1.35, and 12.5 percent and 0.125\">\r\n<thead>\r\n<tr style=\"height: 14px;\" valign=\"top\">\r\n<th style=\"height: 14px; width: 243.125px;\" data-align=\"left\">Percent<\/th>\r\n<th style=\"height: 14px; width: 181.390625px;\" data-align=\"left\">Decimal<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr style=\"height: 14px;\" valign=\"top\">\r\n<td style=\"height: 14px; width: 243.125px;\" data-align=\"left\">[latex]\\text{6%}[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 181.390625px;\" data-align=\"left\">[latex]0.06[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\" valign=\"top\">\r\n<td style=\"height: 14px; width: 243.125px;\" data-align=\"left\">[latex]\\text{78%}[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 181.390625px;\" data-align=\"left\">[latex]0.78[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\" valign=\"top\">\r\n<td style=\"height: 14px; width: 243.125px;\" data-align=\"left\">[latex]\\text{135%}[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 181.390625px;\" data-align=\"left\">[latex]1.35[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\" valign=\"top\">\r\n<td style=\"height: 14px; width: 243.125px;\" data-align=\"left\">[latex]\\text{12.5%}[\/latex]<\/td>\r\n<td style=\"height: 14px; width: 181.390625px;\" data-align=\"left\">[latex]0.125[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\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\" data-number-style=\"arabic\">\r\n \t<li>If possible, convert the fraction to a denominator of [latex]100[\/latex].<\/li>\r\n \t<li>If not, convert the fraction to a decimal by dividing.<\/li>\r\n \t<li>Convert the decimal to a percent.<\/li>\r\n<\/ol>\r\n<\/div>\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 Answer[\/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%.\" data-label=\"\">\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 class=\"alignnone\" 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=\"0.75. Move the decimal point 2 places to the right.\" width=\"41\" height=\"24\" data-media-type=\"image\/png\" \/><\/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%.\" data-label=\"\">\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 class=\"alignnone\" 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=\"1.375. Move the decimal point 2 places to the right.\" width=\"43\" height=\"26\" data-media-type=\"image\/png\" \/><\/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%.\" data-label=\"\">\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>\u00a0[latex]2.2[\/latex]\r\n\r\n<img class=\"alignnone\" 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=\"2.20. Move the decimal point 2 places to the right.\" width=\"45\" height=\"26\" data-media-type=\"image\/png\" \/><\/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\nNotice that we sometimes need to add zeros at the end of the number when moving the decimal two places to the right.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nSometimes when changing a fraction to a decimal, the division continues for many decimal places and we will need to round off the quotient. Typically, you will round before converting to a percent unless instructed otherwise. The number of decimal places we round to will depend on the situation. If the decimal calculation involves money, we round it to the hundredths place. For most other cases, 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>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcome<\/h3>\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Use percent to represent a given fraction or decimal&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:13185,&quot;3&quot;:[null,0],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;,&quot;16&quot;:10}\">Use percent to represent a given fraction or decimal<\/span><\/li>\n<\/ul>\n<\/div>\n<p>How many cents are in one dollar? There are [latex]100[\/latex] cents in a dollar. How many years are in a century? There are [latex]100[\/latex] years in a century. Does this give you a clue about what the word &#8220;percent&#8221; means? It is really two words, &#8220;per cent,&#8221; and means per one hundred. A percent is a ratio whose denominator is [latex]100[\/latex]. We use the percent symbol, [latex]\\%[\/latex], to show percent.<\/p>\n<div class=\"textbox shaded\">\n<h3>Percent<\/h3>\n<p style=\"padding-left: 60px;\">A percent is a ratio whose denominator is [latex]100[\/latex].<\/p>\n<p style=\"padding-left: 60px;\">For example [latex]46\\%=\\Large\\frac{46}{100}[\/latex]<\/p>\n<\/div>\n<p>According to data from the American Association of Community Colleges [latex]\\left(2015\\right)[\/latex], about [latex]\\text{57%}[\/latex] of community college students are female. This means [latex]57[\/latex] out of every [latex]100[\/latex] community college students are female, as the image below\u00a0<span style=\"font-size: 16px;\">shows. Out of the [latex]100[\/latex] squares on the grid, [latex]57[\/latex] are shaded, which we write as the ratio [latex]\\Large\\frac{57}{100}[\/latex].<\/span><\/p>\n<p>Among every [latex]100[\/latex] community college students, [latex]57[\/latex] are female.<\/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\/24221858\/CNX_BMath_Figure_06_01_001.png\" alt=\"The figure shows a hundred flat with 57 units shaded.\" data-media-type=\"image\/png\" \/><br \/>\nSimilarly, [latex]\\text{25%}[\/latex] means a ratio of [latex]\\Large\\frac{25}{100}\\normalsize ,\\text{3%}[\/latex] means a ratio of [latex]\\Large\\frac{3}{100}[\/latex] and [latex]\\text{100%}[\/latex] means a ratio of [latex]\\Large\\frac{100}{100}[\/latex]. In words, &#8220;one hundred percent&#8221; means the total [latex]\\text{100%}[\/latex] is [latex]\\Large\\frac{100}{100}[\/latex], and since [latex]\\Large\\frac{100}{100}\\normalsize =1[\/latex], we see that [latex]\\text{100%}[\/latex] means [latex]1[\/latex] whole.<\/p>\n<p data-type=\"title\">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\" data-number-style=\"arabic\">\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<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=\".\" data-label=\"\">\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. Five hundredths &#8211; 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=\".\" data-label=\"\">\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>Write as a fraction. Eighty-three hundredths &#8211; 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<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>Let&#8217;s look at a few more examples of converting decimals to percents, but these aren&#8217;t as straight forward!<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Convert each decimal to a percent:<br \/>\n1. [latex]0.2[\/latex]<\/p>\n<p>2. [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 Answer<\/span><\/p>\n<div id=\"q740440\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168469711926\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]0.2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write as a fraction. The denominator is [latex]10[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{2}{10}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply the numerator and denominator by [latex]10[\/latex], so that the denominator is [latex]100[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{20}{100}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write this ratio as a percent.<\/td>\n<td>[latex]20\\%[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Notice that you could also have written\u00a0[latex]0.2[\/latex] as\u00a0[latex]0.20[\/latex] and gotten to\u00a0[latex]{\\Large\\frac{20}{100}}[\/latex] without doing any calculations.<\/p>\n<table id=\"eip-id1168468629696\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>2.<\/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]100\\%.[\/latex]<\/p>\n<table id=\"eip-id1168469711926\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>3.<\/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<p>Notice that any decimal that has value beyond the hundredths place will have a decimal answer when converted to a percent.<\/p>\n<\/div>\n<\/div>\n<\/div>\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=\"ohm156959\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=156959&theme=oea&iframe_resize_id=ohm156959&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm156964\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=156964&theme=oea&iframe_resize_id=ohm156964&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Let&#8217;s summarize some of 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 data-align=\"left\">Decimal<\/th>\n<th data-align=\"left\">Percent<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"left\">[latex]0.05[\/latex]<\/td>\n<td data-align=\"left\">[latex]\\text{5%}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">[latex]0.83[\/latex]<\/td>\n<td data-align=\"left\">[latex]\\text{83%}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">[latex]0.2[\/latex]<\/td>\n<td data-align=\"left\">[latex]\\text{20%}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">[latex]1.05[\/latex]<\/td>\n<td data-align=\"left\">[latex]\\text{105%}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">[latex]0.075[\/latex]<\/td>\n<td data-align=\"left\">[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<table id=\"fs-id1166484082063\" style=\"height: 70px;\" summary=\"The table shows two columns and five rows. The first row is a header row and it labels each column. The first column is labeled percent, and the second is labeled decimal. The rows read as follows: 6 percent and 0.06, 78 percent and 0.78, 135 percent and 1.35, and 12.5 percent and 0.125\">\n<thead>\n<tr style=\"height: 14px;\" valign=\"top\">\n<th style=\"height: 14px; width: 243.125px;\" data-align=\"left\">Percent<\/th>\n<th style=\"height: 14px; width: 181.390625px;\" data-align=\"left\">Decimal<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr style=\"height: 14px;\" valign=\"top\">\n<td style=\"height: 14px; width: 243.125px;\" data-align=\"left\">[latex]\\text{6%}[\/latex]<\/td>\n<td style=\"height: 14px; width: 181.390625px;\" data-align=\"left\">[latex]0.06[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\" valign=\"top\">\n<td style=\"height: 14px; width: 243.125px;\" data-align=\"left\">[latex]\\text{78%}[\/latex]<\/td>\n<td style=\"height: 14px; width: 181.390625px;\" data-align=\"left\">[latex]0.78[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\" valign=\"top\">\n<td style=\"height: 14px; width: 243.125px;\" data-align=\"left\">[latex]\\text{135%}[\/latex]<\/td>\n<td style=\"height: 14px; width: 181.390625px;\" data-align=\"left\">[latex]1.35[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\" valign=\"top\">\n<td style=\"height: 14px; width: 243.125px;\" data-align=\"left\">[latex]\\text{12.5%}[\/latex]<\/td>\n<td style=\"height: 14px; width: 181.390625px;\" data-align=\"left\">[latex]0.125[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>In 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\" data-number-style=\"arabic\">\n<li>If possible, convert the fraction to a denominator of [latex]100[\/latex].<\/li>\n<li>If not, convert the fraction to a decimal by dividing.<\/li>\n<li>Convert the decimal to a percent.<\/li>\n<\/ol>\n<\/div>\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 Answer<\/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%.\" data-label=\"\">\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 loading=\"lazy\" decoding=\"async\" class=\"alignnone\" 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=\"0.75. Move the decimal point 2 places to the right.\" width=\"41\" height=\"24\" data-media-type=\"image\/png\" \/><\/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%.\" data-label=\"\">\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 loading=\"lazy\" decoding=\"async\" class=\"alignnone\" 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=\"1.375. Move the decimal point 2 places to the right.\" width=\"43\" height=\"26\" data-media-type=\"image\/png\" \/><\/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%.\" data-label=\"\">\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>\u00a0[latex]2.2[\/latex]<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" 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=\"2.20. Move the decimal point 2 places to the right.\" width=\"45\" height=\"26\" data-media-type=\"image\/png\" \/><\/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<p>Notice that we sometimes need to add zeros at the end of the number when moving the decimal two places to the right.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>Sometimes when changing a fraction to a decimal, the division continues for many decimal places and we will need to round off the quotient. Typically, you will round before converting to a percent unless instructed otherwise. The number of decimal places we round to will depend on the situation. If the decimal calculation involves money, we round it to the hundredths place. For most other cases, 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\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-335\">\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":17,"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":"3dd72215-9cf1-4352-9c17-479ab430838e, f6aebc46-c8b2-43aa-a6ce-6ee36008e15d","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-335","chapter","type-chapter","status-publish","hentry"],"part":22,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters\/335","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":22,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters\/335\/revisions"}],"predecessor-version":[{"id":3988,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters\/335\/revisions\/3988"}],"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\/335\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/media?parent=335"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapter-type?post=335"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/contributor?post=335"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/license?post=335"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}