{"id":342,"date":"2023-02-01T00:04:08","date_gmt":"2023-02-01T00:04:08","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/chapter\/writing-percents-as-fractions-and-decimals\/"},"modified":"2023-02-01T00:04:08","modified_gmt":"2023-02-01T00:04:08","slug":"writing-percents-as-fractions-and-decimals","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/chapter\/writing-percents-as-fractions-and-decimals\/","title":{"raw":"Writing Percents as Fractions and Decimals","rendered":"Writing Percents as Fractions and Decimals"},"content":{"raw":"\n<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n \t<li>Convert a percent to a fraction<\/li>\n \t<li>Convert a percent to a decimal<\/li>\n<\/ul>\n<\/div>\n<h2>Percents [latex]\\longrightarrow[\/latex] Fractions<\/h2>\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].\n<div class=\"textbox shaded\">\n<h3>Convert a percent to a fraction<\/h3>\n<ol id=\"eip-id1168469672602\" class=\"stepwise\">\n \t<li>Write the percent as a ratio with the denominator [latex]100[\/latex].<\/li>\n \t<li>Simplify the fraction if possible.<\/li>\n<\/ol>\n<\/div>\n&nbsp;\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\nConvert each percent to a fraction:\n\n1. [latex]\\text{36%}[\/latex]\n2. [latex]\\text{125%}[\/latex]\n\nSolution\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&nbsp;\n\n<\/div>\n&nbsp;\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n[ohm_question]146657[\/ohm_question]\n\n[ohm_question]146660[\/ohm_question]\n\n<\/div>\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.\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\nConvert each percent to a fraction:\n\n1. [latex]\\text{24.5%}[\/latex]\n2. [latex]33\\Large\\frac{1}{3}\\normalsize\\%[\/latex]\n\nSolution\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&nbsp;\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n[ohm_question]146658[\/ohm_question]\n\n[ohm_question]146659[\/ohm_question]\n\n<\/div>\n<h2>Percents[latex]\\longrightarrow[\/latex]&nbsp;Decimals<\/h2>\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.\n<div class=\"textbox shaded\">\n<h3>Convert a percent to a decimal<\/h3>\n<ol id=\"eip-id1168468771396\" class=\"stepwise\">\n \t<li>Write the percent as a ratio with the denominator [latex]100[\/latex].<\/li>\n \t<li>Convert the fraction to a decimal by dividing the numerator by the denominator.<\/li>\n<\/ol>\n<\/div>\n&nbsp;\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\nConvert each percent to a decimal:\n\n1. [latex]\\text{6%}[\/latex]\n2. [latex]\\text{78%}[\/latex]\n[reveal-answer q=\"113774\"]Show Solution[\/reveal-answer]\n[hidden-answer a=\"113774\"]\n\nSolution\nBecause we want to change to a decimal, we will leave the fractions with denominator [latex]100[\/latex] instead of removing common factors.\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[\/hidden-answer]\n\n<\/div>\n&nbsp;\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\nConvert each percent to a decimal:\n\n1. [latex]\\text{9%}[\/latex]\n2. [latex]\\text{87%}[\/latex]\n\n[reveal-answer q=\"67239\"]Show Solution[\/reveal-answer]\n[hidden-answer a=\"67239\"]\n\n1. [latex]0.09[\/latex]\n2. [latex]0.87[\/latex]\n\n[\/hidden-answer]\n\n<\/div>\n&nbsp;\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\nConvert each percent to a decimal:\n\n1.&nbsp; [latex]\\text{135%}[\/latex]\n2.&nbsp; [latex]\\text{12.5%}[\/latex]\n\nSolution\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&nbsp;\n\n<\/div>\n&nbsp;\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n[ohm_question]146661[\/ohm_question]\n\n[ohm_question]146662[\/ohm_question]\n\n<\/div>\nLet's summarize the results from the previous examples in the&nbsp;table below, and look for a pattern we could use to quickly convert a percent number to a decimal number.\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>\nDo you see the pattern?\n\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.\n\nThe next table&nbsp;uses the percents in the table above&nbsp;and shows visually how to convert them to decimals by moving the decimal point two places to the left.\n\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 \">\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\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.\n<ol>\n \t<li>Convert the percent to a fraction<\/li>\n \t<li>Convert the percent to a decimal<\/li>\n<\/ol>\n[reveal-answer q=\"485409\"]Show Solution[\/reveal-answer]\n[hidden-answer a=\"485409\"]\n\nSolution\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[\/hidden-answer]\n\n<\/div>\n&nbsp;\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n[ohm_question]146663[\/ohm_question]\n\n[ohm_question]146664[\/ohm_question]\n\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\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:\n\n1. a fraction\n2. a decimal\n\nSolution\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&nbsp;\n\n<\/div>\n\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]\n\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n[ohm_question]146665[\/ohm_question]\n\n<\/div>\nIn summary, here is the table from above with conversions of percents to fractions added.\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&nbsp;\n","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]&nbsp;Decimals<\/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.&nbsp; [latex]\\text{135%}[\/latex]<br \/>\n2.&nbsp; [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&nbsp;table 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&nbsp;uses the percents in the table above&nbsp;and 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-342\">\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":538461,"menu_order":4,"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-342","chapter","type-chapter","status-publish","hentry"],"part":338,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/pressbooks\/v2\/chapters\/342","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/wp\/v2\/users\/538461"}],"version-history":[{"count":0,"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/pressbooks\/v2\/chapters\/342\/revisions"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/pressbooks\/v2\/parts\/338"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/pressbooks\/v2\/chapters\/342\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/wp\/v2\/media?parent=342"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=342"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/wp\/v2\/contributor?post=342"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/wp\/v2\/license?post=342"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}