{"id":387,"date":"2021-07-27T14:20:06","date_gmt":"2021-07-27T14:20:06","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=387"},"modified":"2024-01-29T17:44:14","modified_gmt":"2024-01-29T17:44:14","slug":"write-fractions-and-decimals-as-percents","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/write-fractions-and-decimals-as-percents\/","title":{"raw":"Write Fractions and Decimals as Percents","rendered":"Write Fractions and Decimals as Percents"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Convert decimals and fractions to percents<\/li>\r\n<\/ul>\r\n<\/div>\r\nTo convert a decimal to a percent, remember that percent means per hundred and [latex]100 \\%=1 [\/latex]. If we multiply the decimal by [latex]100 \\%[\/latex] we are really multiplying by [latex]1[\/latex].\u00a0 This gives us an easy method to change a decimal to a percent.\r\n<div class=\"textbox shaded\">\r\n<h3>Convert a decimal to a percent<\/h3>\r\n<ol id=\"eip-id1168469368569\" class=\"stepwise\">\r\n \t<li>Multiply the decimal by [latex]100 \\%[\/latex]<\/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<ul>\r\n \t<li>[latex]2.7[\/latex]<\/li>\r\n \t<li>[latex]0.053[\/latex]<\/li>\r\n<\/ul>\r\n[reveal-answer q=\"773608\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"773608\"]\r\n<ul>\r\n \t<li>[latex]2.7=2.7 \\cdot 100 \\% = 270 \\%[\/latex]<\/li>\r\n \t<li>[latex]0.053=0.053 \\cdot 100 \\% = 5.3 \\%[\/latex]<\/li>\r\n<\/ul>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nDo you see a pattern? When we converted a decimal to a percent, we moved the decimal point two places to the right and then inserted a percent sign.\u00a0 Sometimes we need to add zeros at the end of a decimal in order to move the decimal point two places to the right.\r\n<p style=\"text-align: center;\">[latex]0.175=17.5 \\%[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]1.3=1.30=130 \\%[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]0.073=7.3 \\%[\/latex]<\/p>\r\n\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146667[\/ohm_question]\r\n\r\n[ohm_question]146668[\/ohm_question]\r\n\r\n<\/div>\r\nOften in determining a percent, we have a ratio whose denominator is not 100. In order to convert such a ratio to a percent, we first convert the ratio to a decimal.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nIn a survey of 450 residents of a city, 126 said they were dissatisfied with their local internet provider. Find the percent of those surveyed who were not satisfied with their local internet provider.\r\n\r\n[reveal-answer q=\"682251\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"682251\"]\r\n\r\n126 out of 450 residents were not satisfied. This is equivalent to the ratio [latex]\\frac{126}{450}[\/latex].\r\n\r\nTo write a fraction as a decimal, divide the numerator by the denominator.\r\n<p style=\"text-align: center;\">[latex]126 \u00f7 450 = 0.28[\/latex]<\/p>\r\nConvert the decimal to a percent by moving the decimal point two places to the right and inserting a percent symbol.\r\n<p style=\"text-align: center;\">[latex]0.25=28 \\%[\/latex]<\/p>\r\nTherefore, [latex]28 \\%[\/latex] of residents surveyed were not satisfied with their local internet provider.\r\n\r\n[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\n<div class=\"textbox shaded\">\r\n<h3>Convert a fraction to a percent<\/h3>\r\n<ol id=\"eip-id1168467345664\" class=\"stepwise\">\r\n \t<li>Convert the fraction to a decimal<\/li>\r\n \t<li>Convert the decimal to a percent<\/li>\r\n<\/ol>\r\n<\/div>\r\nSometimes when changing a fraction to a decimal, the result continues for many decimal places and we will round off the quotient. The number of decimal places we round to will depend on the situation. If the decimal involves money, we round to the nearest cent (hundredths place). In many 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 exercises\">\r\n<h3>example<\/h3>\r\nWrite as a percent.\u00a0 Round to the nearest tenth of a percent if necessary.\r\n<ul>\r\n \t<li>[latex]\\frac{9}{64}[\/latex]<\/li>\r\n \t<li>[latex]\\frac{2}{3}[\/latex]<\/li>\r\n \t<li>[latex]2 \\frac{3}{4}[\/latex]<\/li>\r\n<\/ul>\r\n[reveal-answer q=\"26083\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"26083\"]\r\n\r\na) To convert [latex]\\frac{9}{64}[\/latex]\u00a0to a percent we first divide the numerator by the denominator to convert to a decimal.\r\n<p style=\"text-align: center;\">[latex]\\frac{9}{64} = 0.140625[\/latex]<\/p>\r\nSince [latex]0.140625[\/latex] rounded to the nearest thousandth is [latex]0.141[\/latex], the percent rounded to the nearest tenth of a percentage point is\r\n<p style=\"text-align: center;\">[latex]0.141=14.1 \\%[\/latex]<\/p>\r\nb) [latex]\\frac{2}{3} = 0.66666...[\/latex]\r\n\r\nRounding to the nearest thousandth and then converting to a percent, we obtain [latex]0.667=66.7 \\%[\/latex]\r\n\r\nc) Note that the mixed number, [latex]2 \\frac{3}{4}[\/latex] means [latex]2 + \\frac{3}{4}[\/latex]. So we have\r\n<p style=\"text-align: center;\">[latex]2 \\frac{3}{4} = 2 + \\frac{3}{4} = 2 + 0.75 = 2.75 = 275 \\%[\/latex]<\/p>\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]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 Outcomes<\/h3>\n<ul>\n<li>Convert decimals and fractions to percents<\/li>\n<\/ul>\n<\/div>\n<p>To convert a decimal to a percent, remember that percent means per hundred and [latex]100 \\%=1[\/latex]. If we multiply the decimal by [latex]100 \\%[\/latex] we are really multiplying by [latex]1[\/latex].\u00a0 This gives us an easy method to change a decimal to a percent.<\/p>\n<div class=\"textbox shaded\">\n<h3>Convert a decimal to a percent<\/h3>\n<ol id=\"eip-id1168469368569\" class=\"stepwise\">\n<li>Multiply the decimal by [latex]100 \\%[\/latex]<\/li>\n<\/ol>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Convert each decimal to a percent:<\/p>\n<ul>\n<li>[latex]2.7[\/latex]<\/li>\n<li>[latex]0.053[\/latex]<\/li>\n<\/ul>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q773608\">Show Answer<\/span><\/p>\n<div id=\"q773608\" class=\"hidden-answer\" style=\"display: none\">\n<ul>\n<li>[latex]2.7=2.7 \\cdot 100 \\% = 270 \\%[\/latex]<\/li>\n<li>[latex]0.053=0.053 \\cdot 100 \\% = 5.3 \\%[\/latex]<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<p>Do you see a pattern? When we converted a decimal to a percent, we moved the decimal point two places to the right and then inserted a percent sign.\u00a0 Sometimes we need to add zeros at the end of a decimal in order to move the decimal point two places to the right.<\/p>\n<p style=\"text-align: center;\">[latex]0.175=17.5 \\%[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]1.3=1.30=130 \\%[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]0.073=7.3 \\%[\/latex]<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146667\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146667&theme=oea&iframe_resize_id=ohm146667&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146668\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146668&theme=oea&iframe_resize_id=ohm146668&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Often in determining a percent, we have a ratio whose denominator is not 100. In order to convert such a ratio to a percent, we first convert the ratio to a decimal.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>In a survey of 450 residents of a city, 126 said they were dissatisfied with their local internet provider. Find the percent of those surveyed who were not satisfied with their local internet provider.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q682251\">Show Answer<\/span><\/p>\n<div id=\"q682251\" class=\"hidden-answer\" style=\"display: none\">\n<p>126 out of 450 residents were not satisfied. This is equivalent to the ratio [latex]\\frac{126}{450}[\/latex].<\/p>\n<p>To write a fraction as a decimal, divide the numerator by the denominator.<\/p>\n<p style=\"text-align: center;\">[latex]126 \u00f7 450 = 0.28[\/latex]<\/p>\n<p>Convert the decimal to a percent by moving the decimal point two places to the right and inserting a percent symbol.<\/p>\n<p style=\"text-align: center;\">[latex]0.25=28 \\%[\/latex]<\/p>\n<p>Therefore, [latex]28 \\%[\/latex] of residents surveyed were not satisfied with their local internet provider.<\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<div class=\"textbox shaded\">\n<h3>Convert a fraction to a percent<\/h3>\n<ol id=\"eip-id1168467345664\" class=\"stepwise\">\n<li>Convert the fraction to a decimal<\/li>\n<li>Convert the decimal to a percent<\/li>\n<\/ol>\n<\/div>\n<p>Sometimes when changing a fraction to a decimal, the result continues for many decimal places and we will round off the quotient. The number of decimal places we round to will depend on the situation. If the decimal involves money, we round to the nearest cent (hundredths place). In many 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 exercises\">\n<h3>example<\/h3>\n<p>Write as a percent.\u00a0 Round to the nearest tenth of a percent if necessary.<\/p>\n<ul>\n<li>[latex]\\frac{9}{64}[\/latex]<\/li>\n<li>[latex]\\frac{2}{3}[\/latex]<\/li>\n<li>[latex]2 \\frac{3}{4}[\/latex]<\/li>\n<\/ul>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q26083\">Show Answer<\/span><\/p>\n<div id=\"q26083\" class=\"hidden-answer\" style=\"display: none\">\n<p>a) To convert [latex]\\frac{9}{64}[\/latex]\u00a0to a percent we first divide the numerator by the denominator to convert to a decimal.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{9}{64} = 0.140625[\/latex]<\/p>\n<p>Since [latex]0.140625[\/latex] rounded to the nearest thousandth is [latex]0.141[\/latex], the percent rounded to the nearest tenth of a percentage point is<\/p>\n<p style=\"text-align: center;\">[latex]0.141=14.1 \\%[\/latex]<\/p>\n<p>b) [latex]\\frac{2}{3} = 0.66666...[\/latex]<\/p>\n<p>Rounding to the nearest thousandth and then converting to a percent, we obtain [latex]0.667=66.7 \\%[\/latex]<\/p>\n<p>c) Note that the mixed number, [latex]2 \\frac{3}{4}[\/latex] means [latex]2 + \\frac{3}{4}[\/latex]. So we have<\/p>\n<p style=\"text-align: center;\">[latex]2 \\frac{3}{4} = 2 + \\frac{3}{4} = 2 + 0.75 = 2.75 = 275 \\%[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\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-387\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Question ID 146671, 146670, 146669, 146668, 146667. <strong>Authored by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, 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>: Access for free at https:\/\/openstax.org\/books\/prealgebra\/pages\/1-introduction<\/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":169134,"menu_order":5,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Access for free at https:\/\/openstax.org\/books\/prealgebra\/pages\/1-introduction\"},{\"type\":\"original\",\"description\":\"Question ID 146671, 146670, 146669, 146668, 146667\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + GPL\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-387","chapter","type-chapter","status-publish","hentry"],"part":23,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/387","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/users\/169134"}],"version-history":[{"count":9,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/387\/revisions"}],"predecessor-version":[{"id":4065,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/387\/revisions\/4065"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/parts\/23"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/387\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=387"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=387"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=387"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=387"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}