{"id":378,"date":"2021-07-27T13:46:50","date_gmt":"2021-07-27T13:46:50","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=378"},"modified":"2022-01-10T18:06:14","modified_gmt":"2022-01-10T18:06:14","slug":"defining-percents","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/defining-percents\/","title":{"raw":"Defining Percents","rendered":"Defining Percents"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Use the definition of percent to write a percent as a ratio and as a decimal<\/li>\r\n<\/ul>\r\n<\/div>\r\nPercents are used in many different applications. They are used widely to describe how something changed. For example, you may have heard that the amount of rainfall this month had decreased by [latex]12\\%[\/latex] from last year, or that the number of jobless claims has increase by [latex]5\\%[\/latex] this quarter over last quarter.\r\n\r\n[caption id=\"attachment_3014\" align=\"aligncenter\" width=\"300\"]<img class=\"wp-image-3014 size-medium\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/117\/2016\/04\/20194605\/Screen-Shot-2016-04-20-at-12.44.43-PM-300x209.png\" alt=\"A graph showing the unemployment rate, with the y-axis representing percent and the x-axis representing time.\" width=\"300\" height=\"209\" \/> Fig. 1: Unemployment rate as percent by year between 2004 and 2014.[\/caption]\r\n\r\nWe regularly use this kind of language to quickly describe how much something increased or decreased over time or between significant events.\r\n\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]\\text{%,}[\/latex] to show percent.\r\n<div class=\"textbox shaded\">\r\n<h3>Percent<\/h3>\r\nA percent is a ratio whose denominator is [latex]100[\/latex]\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.\" \/>\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<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nWrite 37% as a ratio and as a decimal.\r\n\r\n[reveal-answer q=\"501925\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"501925\"]\r\n\r\n37% means a ratio of [latex]\\frac{37}{100}[\/latex]. To write the fraction [latex]\\frac{37}{100}[\/latex] as a decimal, we divide the numerator by the denominator.\r\n<p style=\"text-align: center;\">[latex]37\u00f7100=0.37[\/latex]<\/p>\r\nWhenever we divide a number by 100, the decimal point is moved two places to the left.\r\n<p style=\"text-align: center;\">[latex]3.5 \\% = \\frac{3.5}{100} = 0.035[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]6 \\% = \\frac{6}{100} = 0.06[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]150 \\% = \\frac{150}{100} = 1.5[\/latex]<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox shaded\">\r\n<h3>Write A Percent as a Decimal<\/h3>\r\nTo convert a percent to a decimal, move the decimal point two places to the left and remove the [latex]\\%[\/latex] symbol.\r\n\r\n<\/div>\r\nNote that sometimes we need to insert a decimal point if a percent is stated as a whole number, and sometimes we need to insert leading zeros in order to move the decimal point two places to the left.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nWrite as a decimal.\r\n<ul>\r\n \t<li>[latex]14.7 \\%[\/latex]<\/li>\r\n \t<li>[latex]8.1 \\%[\/latex]<\/li>\r\n \t<li>[latex]200 \\%[\/latex]<\/li>\r\n<\/ul>\r\n[reveal-answer q=\"878765\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"878765\"]\r\n<ul>\r\n \t<li>[latex]14.7 \\% = 0.147[\/latex]<\/li>\r\n \t<li>[latex]8.1 \\% = 0.081[\/latex]<\/li>\r\n \t<li>[latex]200 \\% = 200.0 \\% = 2.000 = 2[\/latex]<\/li>\r\n<\/ul>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try\u00a0it<\/h3>\r\n[ohm_question]146656[\/ohm_question]\r\n\r\n<\/div>\r\nOften when a percent is converted to a ratio, a fraction is obtained which can be simplified. For example, [latex]25 \\% = \\frac{25}{100} = \\frac{25 \\cdot 1}{25 \\cdot 4} = \\frac{1}{4}[\/latex]. Similarly, [latex]40 \\% = \\frac{40}{100} = \\frac{20 \\cdot 2}{20 \\cdot 5} = \\frac{2}{5}[\/latex]","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Use the definition of percent to write a percent as a ratio and as a decimal<\/li>\n<\/ul>\n<\/div>\n<p>Percents are used in many different applications. They are used widely to describe how something changed. For example, you may have heard that the amount of rainfall this month had decreased by [latex]12\\%[\/latex] from last year, or that the number of jobless claims has increase by [latex]5\\%[\/latex] this quarter over last quarter.<\/p>\n<div id=\"attachment_3014\" style=\"width: 310px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-3014\" class=\"wp-image-3014 size-medium\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/117\/2016\/04\/20194605\/Screen-Shot-2016-04-20-at-12.44.43-PM-300x209.png\" alt=\"A graph showing the unemployment rate, with the y-axis representing percent and the x-axis representing time.\" width=\"300\" height=\"209\" \/><\/p>\n<p id=\"caption-attachment-3014\" class=\"wp-caption-text\">Fig. 1: Unemployment rate as percent by year between 2004 and 2014.<\/p>\n<\/div>\n<p>We regularly use this kind of language to quickly describe how much something increased or decreased over time or between significant events.<\/p>\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]\\text{%,}[\/latex] to show percent.<\/p>\n<div class=\"textbox shaded\">\n<h3>Percent<\/h3>\n<p>A percent is a ratio whose denominator is [latex]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.\" \/><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<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Write 37% as a ratio and as a decimal.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q501925\">Show Answer<\/span><\/p>\n<div id=\"q501925\" class=\"hidden-answer\" style=\"display: none\">\n<p>37% means a ratio of [latex]\\frac{37}{100}[\/latex]. To write the fraction [latex]\\frac{37}{100}[\/latex] as a decimal, we divide the numerator by the denominator.<\/p>\n<p style=\"text-align: center;\">[latex]37\u00f7100=0.37[\/latex]<\/p>\n<p>Whenever we divide a number by 100, the decimal point is moved two places to the left.<\/p>\n<p style=\"text-align: center;\">[latex]3.5 \\% = \\frac{3.5}{100} = 0.035[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]6 \\% = \\frac{6}{100} = 0.06[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]150 \\% = \\frac{150}{100} = 1.5[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox shaded\">\n<h3>Write A Percent as a Decimal<\/h3>\n<p>To convert a percent to a decimal, move the decimal point two places to the left and remove the [latex]\\%[\/latex] symbol.<\/p>\n<\/div>\n<p>Note that sometimes we need to insert a decimal point if a percent is stated as a whole number, and sometimes we need to insert leading zeros in order to move the decimal point two places to the left.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Write as a decimal.<\/p>\n<ul>\n<li>[latex]14.7 \\%[\/latex]<\/li>\n<li>[latex]8.1 \\%[\/latex]<\/li>\n<li>[latex]200 \\%[\/latex]<\/li>\n<\/ul>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q878765\">Show Answer<\/span><\/p>\n<div id=\"q878765\" class=\"hidden-answer\" style=\"display: none\">\n<ul>\n<li>[latex]14.7 \\% = 0.147[\/latex]<\/li>\n<li>[latex]8.1 \\% = 0.081[\/latex]<\/li>\n<li>[latex]200 \\% = 200.0 \\% = 2.000 = 2[\/latex]<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try\u00a0it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146656\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146656&theme=oea&iframe_resize_id=ohm146656&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Often when a percent is converted to a ratio, a fraction is obtained which can be simplified. For example, [latex]25 \\% = \\frac{25}{100} = \\frac{25 \\cdot 1}{25 \\cdot 4} = \\frac{1}{4}[\/latex]. Similarly, [latex]40 \\% = \\frac{40}{100} = \\frac{20 \\cdot 2}{20 \\cdot 5} = \\frac{2}{5}[\/latex]<\/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-378\">\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: 146656. <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><li><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><\/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>: 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":4,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"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: 146656\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + GPL\"},{\"type\":\"original\",\"description\":\"\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-378","chapter","type-chapter","status-publish","hentry"],"part":23,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/378","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":12,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/378\/revisions"}],"predecessor-version":[{"id":3209,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/378\/revisions\/3209"}],"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\/378\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=378"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=378"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=378"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=378"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}