{"id":4088,"date":"2020-04-05T21:00:47","date_gmt":"2020-04-05T21:00:47","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=4088"},"modified":"2024-06-26T18:03:34","modified_gmt":"2024-06-26T18:03:34","slug":"writing-percents-as-fractions-and-decimals","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/writing-percents-as-fractions-and-decimals\/","title":{"raw":"Writing Percents as Fractions and Decimals","rendered":"Writing Percents as Fractions and Decimals"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Convert a percent to a fraction<\/li>\r\n \t<li>Convert a percent to a decimal<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Percents [latex]\\longrightarrow[\/latex] Fractions<\/h2>\r\nSince percents are ratios, they can easily be expressed as fractions. Remember that percent means per [latex]100[\/latex], so the denominator of the fraction is [latex]100[\/latex].\r\n<div class=\"textbox shaded\">\r\n<h3>Convert a percent to a fraction<\/h3>\r\n<ol id=\"eip-id1168469672602\" class=\"stepwise\">\r\n \t<li>Write the percent as a ratio with the denominator [latex]100[\/latex].<\/li>\r\n \t<li>Simplify the fraction if possible.<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nConvert each percent to a fraction:\r\n\r\n1. [latex]\\text{36%}[\/latex]\r\n2. [latex]\\text{125%}[\/latex]\r\n\r\nSolution\r\n<table id=\"eip-id1168468456602\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]36\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a ratio with denominator [latex]100[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{36}{100}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]{\\Large\\frac{9}{25}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168468458501\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]125\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a ratio with denominator [latex]100[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{125}{100}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]{\\Large\\frac{5}{4}}[\/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]146657[\/ohm_question]\r\n\r\n[ohm_question]146660[\/ohm_question]\r\n\r\n<\/div>\r\nThe previous example shows that a percent can be greater than [latex]1[\/latex]. We saw that [latex]\\text{125%}[\/latex] means [latex]{\\Large\\frac{125}{100}}[\/latex], or [latex]{\\Large\\frac{5}{4}}[\/latex]. These are improper fractions, and their values are greater than one.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nConvert each percent to a fraction:\r\n\r\n1. [latex]\\text{24.5%}[\/latex]\r\n2. [latex]33\\Large\\frac{1}{3}\\normalsize\\%[\/latex]\r\n\r\nSolution\r\n<table id=\"eip-id1168468250004\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]24.5\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a ratio with denominator [latex]100[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{24.5}{100}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Clear the decimal by multiplying numerator and denominator by [latex]10[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{24.5\\left(10\\right)}{100\\left(10\\right)}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]{\\Large\\frac{245}{1000}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite showing common factors.<\/td>\r\n<td>[latex]{\\Large\\frac{5\\cdot {49}}{5\\cdot {200}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]{\\Large\\frac{49}{200}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168466285175\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]33\\Large\\frac{1}{3}\\normalsize\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a ratio with denominator [latex]100[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{33\\Large\\frac{1}{3}}{100}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the numerator as an improper fraction.<\/td>\r\n<td>[latex]{\\Large\\frac{\\frac{100}{3}}{100}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite as fraction division, replacing [latex]100[\/latex] with [latex]\\frac{100}{1}[\/latex]<\/td>\r\n<td>[latex]{\\Large\\frac{100}{3}}\\div {\\Large\\frac{100}{1}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply by the reciprocal.<\/td>\r\n<td>[latex]{\\Large\\frac{100}{3}} \\cdot {\\Large\\frac{1}{100}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]{\\Large\\frac{1}{3}}[\/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]146658[\/ohm_question]\r\n\r\n[ohm_question]146659[\/ohm_question]\r\n\r\n<\/div>\r\n<h2>Percents[latex]\\longrightarrow[\/latex]\u00a0Decimals<\/h2>\r\nIn Decimals, we learned how to convert fractions to decimals. To convert a percent to a decimal, we first convert it to a fraction and then change the fraction to a decimal.\r\n<div class=\"textbox shaded\">\r\n<h3>Convert a percent to a decimal<\/h3>\r\n<ol id=\"eip-id1168468771396\" class=\"stepwise\">\r\n \t<li>Write the percent as a ratio with the denominator [latex]100[\/latex].<\/li>\r\n \t<li>Convert the fraction to a decimal by dividing the numerator by the denominator.<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nConvert each percent to a decimal:\r\n\r\n1. [latex]\\text{6%}[\/latex]\r\n2. [latex]\\text{78%}[\/latex]\r\n[reveal-answer q=\"113774\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"113774\"]\r\n\r\nSolution\r\nBecause we want to change to a decimal, we will leave the fractions with denominator [latex]100[\/latex] instead of removing common factors.\r\n<table id=\"eip-id1168468510747\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]6\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a ratio with denominator [latex]100[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{6}{100}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Change the fraction to a decimal by dividing the numerator by the denominator.<\/td>\r\n<td>[latex]0.06[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168468668708\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]78\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a ratio with denominator [latex]100[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{78}{100}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Change the fraction to a decimal by dividing the numerator by the denominator.<\/td>\r\n<td>[latex]0.78[\/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\nConvert each percent to a decimal:\r\n\r\n1. [latex]\\text{9%}[\/latex]\r\n2. [latex]\\text{87%}[\/latex]\r\n\r\n[reveal-answer q=\"67239\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"67239\"]\r\n\r\n1. [latex]0.09[\/latex]\r\n2. [latex]0.87[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nConvert each percent to a decimal:\r\n\r\n1.\u00a0 [latex]\\text{135%}[\/latex]\r\n2.\u00a0 [latex]\\text{12.5%}[\/latex]\r\n\r\nSolution\r\n<table id=\"eip-id1168468416060\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]135\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a ratio with denominator [latex]100[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{135}{100}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Change the fraction to a decimal by dividing the numerator by the denominator.<\/td>\r\n<td>[latex]1.35[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168466092208\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]12.5\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a ratio with denominator [latex]100[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{12.5}{100}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Change the fraction to a decimal by dividing the numerator by the denominator.<\/td>\r\n<td>[latex]0.125[\/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]146661[\/ohm_question]\r\n\r\n[ohm_question]146662[\/ohm_question]\r\n\r\n<\/div>\r\nLet's summarize the results from the previous examples in the\u00a0table below, and look for a pattern we could use to quickly convert a percent number to a decimal number.\r\n<table id=\"fs-id1482144\" 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>Percent<\/th>\r\n<th>Decimal<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>[latex]\\text{6%}[\/latex]<\/td>\r\n<td>[latex]0.06[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]\\text{78%}[\/latex]<\/td>\r\n<td>[latex]0.78[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]\\text{135%}[\/latex]<\/td>\r\n<td>[latex]1.35[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]\\text{12.5%}[\/latex]<\/td>\r\n<td>[latex]0.125[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nDo you see the pattern?\r\n\r\nTo convert a percent number to a decimal number, we move the decimal point two places to the left and remove the [latex]%[\/latex] sign. (Sometimes the decimal point does not appear in the percent number, but just like we can think of the integer [latex]6[\/latex] as [latex]6.0[\/latex], we can think of [latex]\\text{6%}[\/latex] as [latex]\\text{6.0%}[\/latex].) Notice that we may need to add zeros in front of the number when moving the decimal to the left.\r\n\r\nThe next table\u00a0uses the percents in the table above\u00a0and shows visually how to convert them to decimals by moving the decimal point two places to the left.\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 figures shows two columns and five rows . The first row is a header row and it labels each column \" \/>\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nAmong a group of business leaders, [latex]\\text{77%}[\/latex] believe that poor math and science education in the U.S. will lead to higher unemployment rates.\r\n<ol>\r\n \t<li>Convert the percent to a fraction<\/li>\r\n \t<li>Convert the percent to a decimal<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"485409\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"485409\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168469469166\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]77\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a ratio with denominator [latex]100[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{77}{100}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168469887983\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]\\Large\\frac{77}{100}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Change the fraction to a decimal by dividing the numerator by the denominator.<\/td>\r\n<td>[latex]0.77[\/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]146663[\/ohm_question]\r\n\r\n[ohm_question]146664[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nThere are four suits of cards in a deck of cards\u2014hearts, diamonds, clubs, and spades. The probability of randomly choosing a heart from a shuffled deck of cards is [latex]\\text{25%}[\/latex]. Convert the percent to:\r\n\r\n1. a fraction\r\n2. a decimal\r\n\r\nSolution\r\n<table id=\"eip-id1168469712021\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]25\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a ratio with denominator [latex]100[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{25}{100}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]{\\Large\\frac{1}{4}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168466986541\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<td>[latex]{\\Large\\frac{1}{4}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Change the fraction to a decimal by dividing the numerator by the denominator.<\/td>\r\n<td>[latex]0.25[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n\r\n<\/div>\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"450\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221902\/CNX_BMath_Figure_06_01_002.png\" alt=\"The figure shows someone holding a deck of cards.\" width=\"450\" height=\"338\" \/> (credit: Riles32807, Wikimedia Commons)[\/caption]\r\n\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146665[\/ohm_question]\r\n\r\n<\/div>\r\nIn summary, here is the table from above with conversions of percents to fractions added.\r\n<table id=\"fs-id1482144\" 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>Percent<\/th>\r\n<th>Decimal<\/th>\r\n<th>Fraction<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>[latex]\\text{6%}[\/latex]<\/td>\r\n<td>[latex]0.06[\/latex]<\/td>\r\n<td>[latex]{\\Large\\frac{3}{50}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]\\text{78%}[\/latex]<\/td>\r\n<td>[latex]0.78[\/latex]<\/td>\r\n<td>[latex]{\\Large\\frac{39}{50}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]\\text{135%}[\/latex]<\/td>\r\n<td>[latex]1.35[\/latex]<\/td>\r\n<td>[latex]{\\Large\\frac{27}{20}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]\\text{12.5%}[\/latex]<\/td>\r\n<td>[latex]0.125[\/latex]<\/td>\r\n<td>[latex]{\\Large\\frac{1}{8}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Convert a percent to a fraction<\/li>\n<li>Convert a percent to a decimal<\/li>\n<\/ul>\n<\/div>\n<h2>Percents [latex]\\longrightarrow[\/latex] Fractions<\/h2>\n<p>Since percents are ratios, they can easily be expressed as fractions. Remember that percent means per [latex]100[\/latex], so the denominator of the fraction is [latex]100[\/latex].<\/p>\n<div class=\"textbox shaded\">\n<h3>Convert a percent to a fraction<\/h3>\n<ol id=\"eip-id1168469672602\" class=\"stepwise\">\n<li>Write the percent as a ratio with the denominator [latex]100[\/latex].<\/li>\n<li>Simplify the fraction if possible.<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Convert each percent to a fraction:<\/p>\n<p>1. [latex]\\text{36%}[\/latex]<br \/>\n2. [latex]\\text{125%}[\/latex]<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168468456602\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<\/tr>\n<tr>\n<td>[latex]36\\%[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write as a ratio with denominator [latex]100[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{36}{100}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]{\\Large\\frac{9}{25}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468458501\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<\/tr>\n<tr>\n<td>[latex]125\\%[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write as a ratio with denominator [latex]100[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{125}{100}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]{\\Large\\frac{5}{4}}[\/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=\"ohm146657\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146657&theme=oea&iframe_resize_id=ohm146657&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146660\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146660&theme=oea&iframe_resize_id=ohm146660&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>The previous example shows that a percent can be greater than [latex]1[\/latex]. We saw that [latex]\\text{125%}[\/latex] means [latex]{\\Large\\frac{125}{100}}[\/latex], or [latex]{\\Large\\frac{5}{4}}[\/latex]. These are improper fractions, and their values are greater than one.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Convert each percent to a fraction:<\/p>\n<p>1. [latex]\\text{24.5%}[\/latex]<br \/>\n2. [latex]33\\Large\\frac{1}{3}\\normalsize\\%[\/latex]<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168468250004\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<\/tr>\n<tr>\n<td>[latex]24.5\\%[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write as a ratio with denominator [latex]100[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{24.5}{100}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Clear the decimal by multiplying numerator and denominator by [latex]10[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{24.5\\left(10\\right)}{100\\left(10\\right)}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]{\\Large\\frac{245}{1000}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite showing common factors.<\/td>\n<td>[latex]{\\Large\\frac{5\\cdot {49}}{5\\cdot {200}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]{\\Large\\frac{49}{200}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168466285175\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<\/tr>\n<tr>\n<td>[latex]33\\Large\\frac{1}{3}\\normalsize\\%[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write as a ratio with denominator [latex]100[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{33\\Large\\frac{1}{3}}{100}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write the numerator as an improper fraction.<\/td>\n<td>[latex]{\\Large\\frac{\\frac{100}{3}}{100}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite as fraction division, replacing [latex]100[\/latex] with [latex]\\frac{100}{1}[\/latex]<\/td>\n<td>[latex]{\\Large\\frac{100}{3}}\\div {\\Large\\frac{100}{1}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply by the reciprocal.<\/td>\n<td>[latex]{\\Large\\frac{100}{3}} \\cdot {\\Large\\frac{1}{100}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]{\\Large\\frac{1}{3}}[\/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=\"ohm146658\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146658&theme=oea&iframe_resize_id=ohm146658&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146659\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146659&theme=oea&iframe_resize_id=ohm146659&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<h2>Percents[latex]\\longrightarrow[\/latex]\u00a0Decimals<\/h2>\n<p>In Decimals, we learned how to convert fractions to decimals. To convert a percent to a decimal, we first convert it to a fraction and then change the fraction to a decimal.<\/p>\n<div class=\"textbox shaded\">\n<h3>Convert a percent to a decimal<\/h3>\n<ol id=\"eip-id1168468771396\" class=\"stepwise\">\n<li>Write the percent as a ratio with the denominator [latex]100[\/latex].<\/li>\n<li>Convert the fraction to a decimal by dividing the numerator by the denominator.<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Convert each percent to a decimal:<\/p>\n<p>1. [latex]\\text{6%}[\/latex]<br \/>\n2. [latex]\\text{78%}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q113774\">Show Solution<\/span><\/p>\n<div id=\"q113774\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nBecause we want to change to a decimal, we will leave the fractions with denominator [latex]100[\/latex] instead of removing common factors.<\/p>\n<table id=\"eip-id1168468510747\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<\/tr>\n<tr>\n<td>[latex]6\\%[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write as a ratio with denominator [latex]100[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{6}{100}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Change the fraction to a decimal by dividing the numerator by the denominator.<\/td>\n<td>[latex]0.06[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468668708\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<\/tr>\n<tr>\n<td>[latex]78\\%[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write as a ratio with denominator [latex]100[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{78}{100}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Change the fraction to a decimal by dividing the numerator by the denominator.<\/td>\n<td>[latex]0.78[\/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>Convert each percent to a decimal:<\/p>\n<p>1. [latex]\\text{9%}[\/latex]<br \/>\n2. [latex]\\text{87%}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q67239\">Show Solution<\/span><\/p>\n<div id=\"q67239\" class=\"hidden-answer\" style=\"display: none\">\n<p>1. [latex]0.09[\/latex]<br \/>\n2. [latex]0.87[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Convert each percent to a decimal:<\/p>\n<p>1.\u00a0 [latex]\\text{135%}[\/latex]<br \/>\n2.\u00a0 [latex]\\text{12.5%}[\/latex]<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168468416060\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<\/tr>\n<tr>\n<td>[latex]135\\%[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write as a ratio with denominator [latex]100[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{135}{100}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Change the fraction to a decimal by dividing the numerator by the denominator.<\/td>\n<td>[latex]1.35[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168466092208\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<\/tr>\n<tr>\n<td>[latex]12.5\\%[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write as a ratio with denominator [latex]100[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{12.5}{100}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Change the fraction to a decimal by dividing the numerator by the denominator.<\/td>\n<td>[latex]0.125[\/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=\"ohm146661\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146661&theme=oea&iframe_resize_id=ohm146661&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146662\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146662&theme=oea&iframe_resize_id=ohm146662&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\u00a0table below, and look for a pattern we could use to quickly convert a percent number to a decimal number.<\/p>\n<table id=\"fs-id1482144\" 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>Percent<\/th>\n<th>Decimal<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>[latex]\\text{6%}[\/latex]<\/td>\n<td>[latex]0.06[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]\\text{78%}[\/latex]<\/td>\n<td>[latex]0.78[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]\\text{135%}[\/latex]<\/td>\n<td>[latex]1.35[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]\\text{12.5%}[\/latex]<\/td>\n<td>[latex]0.125[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Do you see the pattern?<\/p>\n<p>To convert a percent number to a decimal number, we move the decimal point two places to the left and remove the [latex]%[\/latex] sign. (Sometimes the decimal point does not appear in the percent number, but just like we can think of the integer [latex]6[\/latex] as [latex]6.0[\/latex], we can think of [latex]\\text{6%}[\/latex] as [latex]\\text{6.0%}[\/latex].) Notice that we may need to add zeros in front of the number when moving the decimal to the left.<\/p>\n<p>The next table\u00a0uses the percents in the table above\u00a0and shows visually how to convert them to decimals by moving the decimal point two places to the left.<\/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 figures shows two columns and five rows . The first row is a header row and it labels each column\" \/><\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Among a group of business leaders, [latex]\\text{77%}[\/latex] believe that poor math and science education in the U.S. will lead to higher unemployment rates.<\/p>\n<ol>\n<li>Convert the percent to a fraction<\/li>\n<li>Convert the percent to a decimal<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q485409\">Show Solution<\/span><\/p>\n<div id=\"q485409\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168469469166\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<\/tr>\n<tr>\n<td>[latex]77\\%[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write as a ratio with denominator [latex]100[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{77}{100}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168469887983\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<\/tr>\n<tr>\n<td>[latex]\\Large\\frac{77}{100}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Change the fraction to a decimal by dividing the numerator by the denominator.<\/td>\n<td>[latex]0.77[\/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=\"ohm146663\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146663&theme=oea&iframe_resize_id=ohm146663&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146664\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146664&theme=oea&iframe_resize_id=ohm146664&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>There are four suits of cards in a deck of cards\u2014hearts, diamonds, clubs, and spades. The probability of randomly choosing a heart from a shuffled deck of cards is [latex]\\text{25%}[\/latex]. Convert the percent to:<\/p>\n<p>1. a fraction<br \/>\n2. a decimal<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168469712021\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<\/tr>\n<tr>\n<td>[latex]25\\%[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write as a ratio with denominator [latex]100[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{25}{100}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]{\\Large\\frac{1}{4}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168466986541\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<td>[latex]{\\Large\\frac{1}{4}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Change the fraction to a decimal by dividing the numerator by the denominator.<\/td>\n<td>[latex]0.25[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<\/div>\n<div style=\"width: 460px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221902\/CNX_BMath_Figure_06_01_002.png\" alt=\"The figure shows someone holding a deck of cards.\" width=\"450\" height=\"338\" \/><\/p>\n<p class=\"wp-caption-text\">(credit: Riles32807, Wikimedia Commons)<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146665\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146665&theme=oea&iframe_resize_id=ohm146665&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In summary, here is the table from above with conversions of percents to fractions added.<\/p>\n<table id=\"fs-id1482144\" 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>Percent<\/th>\n<th>Decimal<\/th>\n<th>Fraction<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>[latex]\\text{6%}[\/latex]<\/td>\n<td>[latex]0.06[\/latex]<\/td>\n<td>[latex]{\\Large\\frac{3}{50}}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]\\text{78%}[\/latex]<\/td>\n<td>[latex]0.78[\/latex]<\/td>\n<td>[latex]{\\Large\\frac{39}{50}}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]\\text{135%}[\/latex]<\/td>\n<td>[latex]1.35[\/latex]<\/td>\n<td>[latex]{\\Large\\frac{27}{20}}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]\\text{12.5%}[\/latex]<\/td>\n<td>[latex]0.125[\/latex]<\/td>\n<td>[latex]{\\Large\\frac{1}{8}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/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-4088\">\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: 146665, 146664, 146665, 146663, 146662, 146661. <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":7,"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: 146665, 146664, 146665, 146663, 146662, 146661\",\"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-4088","chapter","type-chapter","status-publish","hentry"],"part":5569,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4088","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/users\/25777"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4088\/revisions"}],"predecessor-version":[{"id":4097,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4088\/revisions\/4097"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/parts\/5569"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4088\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=4088"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=4088"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=4088"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=4088"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}