{"id":34,"date":"2021-07-29T16:17:23","date_gmt":"2021-07-29T20:17:23","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/alfm6\/?post_type=chapter&#038;p=34"},"modified":"2022-03-31T10:42:06","modified_gmt":"2022-03-31T14:42:06","slug":"introducing-percent","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/alfm6\/chapter\/introducing-percent\/","title":{"raw":"Topic A: Introducing Percent","rendered":"Topic A: Introducing Percent"},"content":{"raw":"<h1>Reading and Writing Percents<\/h1>\r\n<strong>To write a percent:<\/strong>\r\n<ul>\r\n \t<li>Write the number in the usual way<\/li>\r\n \t<li>Place the percent sign after the numerals\r\n<ul>\r\n \t<li>[latex]50\\%[\/latex]<\/li>\r\n \t<li>[latex]5\\frac{1}{2}\\%[\/latex] or [latex]5.5\\%[\/latex]<\/li>\r\n \t<li>[latex]\\frac{3}{4}\\%[\/latex] or [latex]0.75\\%[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<strong>To read a percent:<\/strong>\r\n<ul>\r\n \t<li>Read the numbers in the usual way<\/li>\r\n \t<li>Say \u201cpercent\" after the number\r\n<ul>\r\n \t<li>[latex]16\\%[\/latex]: say \u201csixteen percent\"<\/li>\r\n \t<li>[latex]4\\frac{1}{2}\\%[\/latex]: say \"four and one-half percent\"<\/li>\r\n \t<li>[latex]0.25\\%[\/latex]: say \"twenty-five hundredths percent,\" or \u201cone-quarter percent,\" or \u201cpoint two five percent\"<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n&nbsp;\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nWrite these percents using numerals and a percent sign. Note that the mixed numbers may be expressed with common fractions or decimals.\r\n<ol type=\"A\">\r\n \t<li>Thirty-four percent <span aria-label=\"blank;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>[latex]34\\%[\/latex]<\/li>\r\n \t<li>Twelve percent<\/li>\r\n \t<li>Four-fifths percent<\/li>\r\n \t<li>One hundred sixteen and three-tenths percent<\/li>\r\n \t<li>Thirteen percent<\/li>\r\n \t<li>Six and one-fifth percent<\/li>\r\n \t<li>Ninety-four and one-half percent<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 1<\/strong>\r\n<ol start=\"2\" type=\"A\">\r\n \t<li>[latex]12\\%[\/latex]<\/li>\r\n \t<li>[latex]0.8\\%[\/latex] or [latex]\\frac{4}{5}\\%[\/latex]<\/li>\r\n \t<li>[latex]116.3\\%[\/latex] or [latex]116\\frac{3}{10}\\%[\/latex]<\/li>\r\n \t<li>[latex]13\\%[\/latex]<\/li>\r\n \t<li>[latex]6.2\\%[\/latex] or [latex]6\\frac{1}{5}\\%[\/latex]<\/li>\r\n \t<li>[latex]94.5\\%[\/latex] or [latex]94\\frac{1}{2}\\%[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<ol type=\"A\">\r\n \t<li>[latex]62\\%[\/latex] <span aria-label=\"blank;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span><span aria-label=\"blank;\">sixty-two percent<\/span><\/li>\r\n \t<li>[latex]37\\frac{1}{2}\\%[\/latex]<\/li>\r\n \t<li>[latex]202\\%[\/latex]<\/li>\r\n \t<li>[latex]\\frac{3}{4}\\%[\/latex]<\/li>\r\n \t<li>[latex]18.3\\%[\/latex]<\/li>\r\n \t<li>[latex]14\\frac{1}{2}\\%[\/latex]<\/li>\r\n \t<li>[latex]100\\frac{1}{2}\\%[\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 2<\/strong>\r\n<ol start=\"2\" type=\"A\">\r\n \t<li>Thirty-seven and one-half percent<\/li>\r\n \t<li>Two hundred two percent<\/li>\r\n \t<li>Three-quarters percent<\/li>\r\n \t<li>Eighteen and three-tenths percent<\/li>\r\n \t<li>Five-tenths percent or one-half percent or zero point five percent<\/li>\r\n \t<li>One hundred percent<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h1>Changing Decimals to Percents<\/h1>\r\nWriting equivalent fractions is an important math skill.\r\n\r\nEquivalent common fractions, decimals, and percents all represent the same amount.\r\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%; height: 48px;\" border=\"0\"><caption>Equivalent fractions, decimals, and percentages<\/caption>\r\n<tbody>\r\n<tr style=\"height: 16px;\">\r\n<th style=\"width: 33.3333%; height: 16px;\" scope=\"col\">Fractions<\/th>\r\n<th style=\"width: 33.3333%; height: 16px;\" scope=\"col\">Decimals<\/th>\r\n<th style=\"width: 33.3333%; height: 16px;\" scope=\"col\">Percentages<\/th>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 33.3333%; height: 16px;\">[latex]\\frac{1}{2}[\/latex]<\/td>\r\n<td style=\"width: 33.3333%; height: 16px;\">[latex]0.5[\/latex]<\/td>\r\n<td style=\"width: 33.3333%; height: 16px;\">[latex]50\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 33.3333%; height: 16px;\">[latex]\\frac{3}{10}[\/latex]<\/td>\r\n<td style=\"width: 33.3333%; height: 16px;\">[latex]0.3[\/latex]<\/td>\r\n<td style=\"width: 33.3333%; height: 16px;\">[latex]30\\%[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nYou need the skill of writing equivalent fractions for working with percents.\r\n<div class=\"textbox shaded\">To change any number to a percent, multiply the number by 100% and place a percent sign % after the product.<\/div>\r\n&nbsp;\r\n\r\nRemember this shortcut for multiplying by 100?\r\n<p style=\"text-align: center;\">[latex]4.27\\times100=427[\/latex]\r\n[latex]0.287\\times100=28.7[\/latex]\r\n[latex]53\\times100=5300[\/latex]<\/p>\r\nThe shortcut is: <strong>When multiplying by 100, move the decimal point two places to the right.<\/strong>\r\n\r\n&nbsp;\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example A<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">Change these numbers to a percent.[latex]\\begin{equation}\\begin{split}\r\n&amp;1 \\ \\ \\ \\ \\ \\ \\ \\ &amp;1\\times100\\% \\ \\ \\ \\ &amp;= \\ \\ \\ \\ &amp;100\\% \\\\\r\n&amp;0.25 \\ \\ \\ \\ \\ \\ \\ &amp;0.25\\times100\\% \\ \\ \\ \\ &amp;= \\ \\ \\ \\ &amp;25\\% \\\\\r\n&amp;0.8 \\ \\ \\ \\ \\ \\ \\ &amp;0.8\\times100\\% \\ \\ \\ \\ &amp;= \\ \\ \\ \\ &amp;80\\% \\\\\r\n&amp;0.375 \\ \\ \\ \\ \\ \\ \\ &amp;0.375\\times100\\% \\ \\ \\ \\ &amp;= \\ \\ \\ \\ &amp;37.5\\% \\\\\r\n\\end{split}\\end{equation}[\/latex]<\/div>\r\n<\/div>\r\n&nbsp;\r\n\r\nSo...\r\n\r\n&nbsp;\r\n<div class=\"textbox shaded\">To change a decimal to a percent, move the decimal point two places to the right and then write the percent sign after the number.<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example B<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">Change each decimal to a percent.<\/div>\r\n<div class=\"textbox__content\">[latex]\r\n\\begin{equation}\\begin{split}\r\n&amp;\\curvearrowright \\\\\r\n0.125=0&amp;.125=12.5\\%\r\n\\end{split}\\end{equation}[\/latex]<\/div>\r\n<div class=\"textbox__content\">[latex]\r\n\\begin{equation}\\begin{split}\r\n&amp;\\curvearrowright \\\\\r\n1.375=1&amp;.375=137.5\\%\r\n\\end{split}\\end{equation}[\/latex]<\/div>\r\n<\/div>\r\n&nbsp;\r\n\r\nIf the decimal point moves to the end of the number it is not necessary to write the decimal point. Remember that zeros at the beginning of a number are also not necessary.\r\n\r\n[latex]\r\n\\begin{equation}\\begin{split}\r\n&amp;\\curvearrowright \\\\\r\n0.24=0&amp;.24=\\cancel{0}.24\\%=24\\%\r\n\\end{split}\\end{equation}[\/latex]\r\n\r\n[latex]\r\n\\begin{equation}\\begin{split}\r\n&amp;\\curvearrowright \\\\\r\n0.05=0&amp;.05=\\cancel{0.0}5\\%=5\\%\r\n\\end{split}\\end{equation}[\/latex]\r\n\r\nIf the decimal is a tenth (one decimal place), it will be necessary to add a zero. If you are changing a whole number to a percent, add two zeros.\r\n\r\n[latex]\r\n\\begin{equation}\\begin{split}\r\n&amp;\\curvearrowright \\\\\r\n0.4=0&amp;.40=40\\%\r\n\\end{split}\\end{equation}[\/latex]\r\n\r\n[latex]\r\n\\begin{equation}\\begin{split}\r\n&amp;\\curvearrowright \\\\\r\n1.7=1&amp;.70=170\\%\r\n\\end{split}\\end{equation}[\/latex]\r\n\r\n[latex]\r\n\\begin{equation}\\begin{split}\r\n&amp;\\curvearrowright \\\\\r\n2=2&amp;.00=200\\%\r\n\\end{split}\\end{equation}[\/latex]\r\n\r\n&nbsp;\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nChange these decimals to percents.\r\n<table style=\"border-collapse: collapse; width: 100%;\">\r\n<tbody>\r\n<tr>\r\n<th style=\"width: 15%; text-align: center;\" scope=\"col\"><\/th>\r\n<th style=\"width: 25%; text-align: center; vertical-align: top;\" scope=\"col\">Decimal<\/th>\r\n<th style=\"width: 35%; text-align: center; vertical-align: top;\" scope=\"col\">\u00d7 100%\r\nMove decimal 2 places to right<\/th>\r\n<th style=\"width: 25%; text-align: center; vertical-align: top;\" scope=\"col\">= Percent<\/th>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 15%; text-align: center;\" scope=\"row\">A.<\/th>\r\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]0.75[\/latex]<\/td>\r\n<td style=\"width: 35%; text-align: center;\" scope=\"col\">[latex]\\begin{equation}\\begin{split}\r\n&amp;\\curvearrowright \\\\\r\n0&amp;.75\r\n\\end{split}\\end{equation}[\/latex]<\/td>\r\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]=75\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 15%; text-align: center;\" scope=\"row\">B.<\/th>\r\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]0.33[\/latex]<\/td>\r\n<td style=\"width: 35%; text-align: center;\" scope=\"col\"><\/td>\r\n<td style=\"width: 25%; text-align: center;\" scope=\"col\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 15%; text-align: center;\" scope=\"row\">C.<\/th>\r\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]0.1[\/latex]<\/td>\r\n<td style=\"width: 35%; text-align: center;\" scope=\"col\"><\/td>\r\n<td style=\"width: 25%; text-align: center;\" scope=\"col\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 15%; text-align: center;\" scope=\"row\">D.<\/th>\r\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]0.0025[\/latex]<\/td>\r\n<td style=\"width: 35%; text-align: center;\" scope=\"col\"><\/td>\r\n<td style=\"width: 25%; text-align: center;\" scope=\"col\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 15%; text-align: center;\" scope=\"row\">E.<\/th>\r\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]0.9[\/latex]<\/td>\r\n<td style=\"width: 35%; text-align: center;\" scope=\"col\"><\/td>\r\n<td style=\"width: 25%; text-align: center;\" scope=\"col\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 15%; text-align: center;\" scope=\"row\">F.<\/th>\r\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]0.325[\/latex]<\/td>\r\n<td style=\"width: 35%; text-align: center;\" scope=\"col\"><\/td>\r\n<td style=\"width: 25%; text-align: center;\" scope=\"col\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 15%; text-align: center;\" scope=\"row\">G.<\/th>\r\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]0.0625[\/latex]<\/td>\r\n<td style=\"width: 35%; text-align: center;\" scope=\"col\"><\/td>\r\n<td style=\"width: 25%; text-align: center;\" scope=\"col\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 15%; text-align: center;\" scope=\"row\">H.<\/th>\r\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]3[\/latex]<\/td>\r\n<td style=\"width: 35%; text-align: center;\" scope=\"col\"><\/td>\r\n<td style=\"width: 25%; text-align: center;\" scope=\"col\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<strong>Answers to Exercise 3<\/strong>\r\n<ol start=\"2\" type=\"A\">\r\n \t<li>[latex]33\\%[\/latex]<\/li>\r\n \t<li>[latex]10\\%[\/latex]<\/li>\r\n \t<li>[latex]0.25\\%[\/latex]<\/li>\r\n \t<li>[latex]90\\%[\/latex]<\/li>\r\n \t<li>[latex]32.5\\%[\/latex]<\/li>\r\n \t<li>[latex]6.25\\%[\/latex]<\/li>\r\n \t<li>[latex]300\\%[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n<h1>Changing Percents to Decimals<\/h1>\r\nReview dividing by 100:\r\n<p style=\"text-align: center;\">[latex]47.39\\div100=0.4739[\/latex]\r\n[latex]429\\div100=4.29[\/latex]\r\n[latex]3.824\\div100=0.03824[\/latex]<\/p>\r\n<strong>To divide by 100, move the decimal point two places to the left.<\/strong>\r\n\r\n&nbsp;\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example A<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nChange each percent to a decimal or mixed number.\r\n\r\n[latex]\\begin{equation}\\begin{split}\r\n58\\% \\ \\ &amp;= \\ \\ 58\\div100 \\ \\ &amp;= \\ \\ .58 \\ \\ &amp;= \\ \\ 0.58 \\\\\r\n20\\% \\ \\ &amp;= \\ \\ 20\\div100 \\ \\ &amp;= \\ \\ .2 \\ \\ &amp;= \\ \\ 0.2 \\\\\r\n6\\% \\ \\ &amp;= \\ \\ 6\\div100 \\ \\ &amp;= \\ \\ .06 \\ \\ &amp;= \\ \\ 0.06 \\\\\r\n110\\% \\ \\ &amp;= \\ \\ 110\\div100 \\ \\ &amp;= \\ \\ 1.10\r\n\\end{split}\\end{equation}[\/latex]\r\n\r\n<\/div>\r\n<\/div>\r\nSo...\r\n<div class=\"textbox shaded\">To change a percent to a decimal, divide by 100 (move the decimal point two places to the <strong>left<\/strong>) and remove the percent sign.<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example B<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nChange each percent to a decimal.\r\n\r\n[latex]\\begin{equation}\\begin{split}\r\n75\\% \\ \\ &amp;= \\ \\ 75.0\\% \\ \\ &amp;= \\ \\ 0.75 \\\\\r\n12\\% \\ \\ &amp;= \\ \\ 12.0\\% \\ \\ &amp;= \\ \\ 0.12 \\\\\r\n37.5\\% \\ \\ &amp;= \\ \\ 37.5\\% \\ \\ &amp;= \\ \\ 0.375 \\\\\r\n125\\% \\ \\ &amp;= \\ \\ 125.0\\% \\ \\ &amp;= \\ \\ 1.25 \\\\\r\n5\\% \\ \\ &amp;= \\ \\ 5.0\\% \\ \\ &amp;= \\ \\ 0.05 \\\\\r\n4.6\\% \\ \\ &amp;= \\ \\ 4.6\\% \\ \\ &amp;= \\ \\ 0.046 \\\\\r\n\\end{split}\\end{equation}[\/latex]\r\n\r\n<\/div>\r\n<\/div>\r\nSome notes to remember:\r\n<ul>\r\n \t<li>If there is no decimal point in the percent, place the decimal point <strong>after<\/strong> the last numeral and <strong>then<\/strong> divide by 100.[latex]24\\%=24.0\\%=0.24[\/latex]<\/li>\r\n \t<li>It may be necessary to <strong>prefix<\/strong> zeros. (This means adding zeros in front of the number, if needed).[latex]6\\%=6.0\\%=0.06[\/latex]<\/li>\r\n \t<li>A zero at the right of a decimal is not needed and may be left off.[latex]40\\%=40.0\\%=0.40=0.4[\/latex]<\/li>\r\n<\/ul>\r\n&nbsp;\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 4<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nChange each percent to its decimal equivalent.\r\n<table style=\"border-collapse: collapse; width: 100%;\">\r\n<tbody>\r\n<tr>\r\n<th style=\"width: 15%; text-align: center;\" scope=\"col\"><\/th>\r\n<th style=\"width: 25%; text-align: center; vertical-align: top;\" scope=\"col\">Percent<\/th>\r\n<th style=\"width: 35%; text-align: center; vertical-align: top;\" scope=\"col\">\u00f7 100%\r\nMove decimal 2 places to left<\/th>\r\n<th style=\"width: 25%; text-align: center; vertical-align: top;\" scope=\"col\">= Decimal<\/th>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 15%; text-align: center;\" scope=\"row\">A.<\/th>\r\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]23\\%[\/latex]<\/td>\r\n<td style=\"width: 35%; text-align: center;\" scope=\"col\">[latex]\\begin{equation}\\begin{split}\r\n&amp;\\curvearrowleft \\\\\r\n&amp; \\ 23.\r\n\\end{split}\\end{equation}[\/latex]<\/td>\r\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]=0.23[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 15%; text-align: center;\" scope=\"row\">B.<\/th>\r\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]1\\%[\/latex]<\/td>\r\n<td style=\"width: 35%; text-align: center;\" scope=\"col\"><\/td>\r\n<td style=\"width: 25%; text-align: center;\" scope=\"col\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 15%; text-align: center;\" scope=\"row\">C.<\/th>\r\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]112\\%[\/latex]<\/td>\r\n<td style=\"width: 35%; text-align: center;\" scope=\"col\"><\/td>\r\n<td style=\"width: 25%; text-align: center;\" scope=\"col\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 15%; text-align: center;\" scope=\"row\">D.<\/th>\r\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]10.3\\%[\/latex]<\/td>\r\n<td style=\"width: 35%; text-align: center;\" scope=\"col\"><\/td>\r\n<td style=\"width: 25%; text-align: center;\" scope=\"col\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 15%; text-align: center;\" scope=\"row\">E.<\/th>\r\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]36\\%[\/latex]<\/td>\r\n<td style=\"width: 35%; text-align: center;\" scope=\"col\"><\/td>\r\n<td style=\"width: 25%; text-align: center;\" scope=\"col\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 15%; text-align: center;\" scope=\"row\">F.<\/th>\r\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]147\\%[\/latex]<\/td>\r\n<td style=\"width: 35%; text-align: center;\" scope=\"col\"><\/td>\r\n<td style=\"width: 25%; text-align: center;\" scope=\"col\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<strong>Answers to Exercise 4<\/strong>\r\n<ol start=\"2\" type=\"A\">\r\n \t<li>[latex]0.01[\/latex]<\/li>\r\n \t<li>[latex]1.12[\/latex]<\/li>\r\n \t<li>[latex]0.103[\/latex]<\/li>\r\n \t<li>[latex]0.36[\/latex]<\/li>\r\n \t<li>[latex]1.47[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<strong>To change a percent containing a common fraction to a decimal<\/strong>, do this:\r\n<ul>\r\n \t<li>Change the common fraction in the percent to a decimal in the percent.<\/li>\r\n \t<li>Divide by 100 (move the decimal 2 places to the <strong>left<\/strong>).<\/li>\r\n<\/ul>\r\n&nbsp;\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example C<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">[latex]\\begin{equation}\\begin{split}\r\n3\\tfrac{1}{2}\\% \\ \\ &amp;= \\ \\ 3.5\\% \\ \\ \\ \\ \\ \\ \\ &amp;3.5\\% &amp;\\div 100 \\ &amp;= .035 &amp;= 0.035 \\\\\r\n37\\tfrac{1}{2}\\% \\ \\ &amp;= \\ \\ 37.5\\% \\ \\ \\ \\ \\ \\ \\ &amp;37.5\\% &amp;\\div 100 \\ &amp;= .375 &amp;= 0.375 \\\\\r\n\\tfrac{1}{4}\\% \\ \\ &amp;= \\ \\ 0.25\\% \\ \\ \\ \\ \\ \\ \\ &amp;0.25\\% &amp;\\div 100 \\ &amp;= .0025 \\\\\r\n17\\tfrac{1}{3}\\% \\ \\ &amp;= \\ \\ 17.\\overline{3}\\% \\ \\ \\ \\ \\ \\ \\ &amp;17.\\overline{3}\\% &amp;\\div 100 \\ &amp;= 0.17\\overline{3}\r\n\\end{split}\\end{equation}[\/latex]<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 5<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nChange each percent to its decimal equivalent.\r\n<ol type=\"A\">\r\n \t<li>[latex]8\\frac{4}{5}\\%= \\ \\ \\ \\ \\ 8.8\\%=0.088[\/latex]<\/li>\r\n \t<li>[latex]4\\frac{1}{2}\\%= [\/latex]<\/li>\r\n \t<li>[latex]56\\frac{3}{4}\\%= [\/latex]<\/li>\r\n \t<li>[latex]1\\frac{3}{5}\\%= [\/latex]<\/li>\r\n \t<li>[latex]112\\frac{1}{2}\\%= [\/latex]<\/li>\r\n \t<li>[latex]2\\frac{3}{8}\\%= [\/latex]<\/li>\r\n \t<li>[latex]5\\frac{1}{4}\\%= [\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 5<\/strong>\r\n<ol start=\"2\" type=\"A\">\r\n \t<li>[latex]0.045[\/latex]<\/li>\r\n \t<li>[latex]0.5675[\/latex]<\/li>\r\n \t<li>[latex]0.016[\/latex]<\/li>\r\n \t<li>[latex]1.125[\/latex]<\/li>\r\n \t<li>[latex]0.02375[\/latex]<\/li>\r\n \t<li>[latex]0.0525[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n<h1>Changing Common Fractions to Percents<\/h1>\r\n<div class=\"textbox shaded\">To change any number to a percent, multiply the number by 100% and place the percent sign % after the product.<\/div>\r\nThere are two methods you can use to change a common fraction to a percent.\r\n<h2>Method One:<\/h2>\r\nTo change a common fraction to an equivalent percent, <strong>multiply the common fraction by 100%.<\/strong>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example A<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">[latex]\\frac{3}{4} = \\text{_____}\\%[\/latex]<\/div>\r\n<div class=\"textbox__content\">\r\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%; height: 147px;\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 36.8881%;\"><\/td>\r\n<td style=\"width: 38.1119%; height: 16px;\">[latex]\\frac{3}{4}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 36.8881%;\">Multiply by 100%<\/td>\r\n<td style=\"width: 38.1119%; height: 33px;\">[latex]\\frac{3}{4} \\times 100\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 36.8881%;\">Convert 100% to a fraction.<\/td>\r\n<td style=\"width: 38.1119%; height: 33px;\">[latex]\\frac{3}{4} \\times \\frac{100}{1}\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 36.8881%;\">Simplify the fractions by dividing the numerator and denominator by 4.<\/td>\r\n<td style=\"width: 38.1119%;\">[latex]\\frac{3}{\\cancel{4}1} \\times \\frac{\\cancel{100}25}{1}\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 36.8881%;\">The 4 cancels and 100 is reduced to 25.<\/td>\r\n<td style=\"width: 38.1119%; height: 33px;\">[latex]\\frac{3}{1} \\times \\frac{25}{1}\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 36.8881%;\">Multiply 3 by 25%.<\/td>\r\n<td style=\"width: 38.1119%; height: 16px;\">[latex]3 \\times 25\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 36.8881%;\"><\/td>\r\n<td style=\"width: 38.1119%; height: 16px;\">[latex]75\\%[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<div><\/div>\r\n<div class=\"textbox__content\">[latex]1\\frac{1}{5} = \\text{_____}\\%[\/latex]<\/div>\r\n<div class=\"textbox__content\">\r\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 36.7133%;\"><\/td>\r\n<td style=\"width: 38.2867%;\">[latex]1\\frac{1}{5}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 36.7133%;\">Convert number to a fraction.<\/td>\r\n<td style=\"width: 38.2867%;\">[latex]\\frac{6}{5}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 36.7133%;\">Multiply by 100%.<\/td>\r\n<td style=\"width: 38.2867%;\">[latex]\\frac{6}{5} \\times 100\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 36.7133%;\">Convert 100% to a fraction.<\/td>\r\n<td style=\"width: 38.2867%;\">[latex]\\frac{6}{5} \\times \\frac{100}{1}\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 36.7133%;\">Simplify the fractions by dividing the denominator and numerator by 5.<\/td>\r\n<td style=\"width: 38.2867%;\">[latex]\\frac{6}{\\cancel{5}1} \\times \\frac{\\cancel{100}20}{1}\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 36.7133%;\">The 5 cancels and 100 is reduced to 20.<\/td>\r\n<td style=\"width: 38.2867%;\">[latex]\\frac{6}{1} \\times \\frac{20}{1}\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 36.7133%;\">Multiply 6 by 20%.<\/td>\r\n<td style=\"width: 38.2867%;\">[latex]6 \\times 20\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 36.7133%;\"><\/td>\r\n<td style=\"width: 38.2867%;\">[latex]120\\%[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 6<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nMultiply by 100% to change each common fraction to an equivalent percent.\r\n<ol type=\"A\">\r\n \t<li>[latex]\\frac{4}{5} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\frac{4}{5}\\times100\\%=80\\%[\/latex]<\/li>\r\n \t<li>[latex]\\frac{1}{5}\\%= [\/latex]<\/li>\r\n \t<li>[latex]\\frac{9}{10}\\%= [\/latex]<\/li>\r\n \t<li>[latex]1\\frac{1}{2}\\%= [\/latex]<\/li>\r\n \t<li>[latex]\\frac{7}{10}\\%= [\/latex]<\/li>\r\n \t<li>[latex]3\\frac{3}{4}\\%= [\/latex]<\/li>\r\n \t<li>[latex]\\frac{1}{2}\\%= [\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 6<\/strong>\r\n<ol start=\"2\" type=\"A\">\r\n \t<li>[latex]20\\%[\/latex]<\/li>\r\n \t<li>[latex]90\\%[\/latex]<\/li>\r\n \t<li>[latex]150\\%[\/latex]<\/li>\r\n \t<li>[latex]70\\%[\/latex]<\/li>\r\n \t<li>[latex]375\\%[\/latex]<\/li>\r\n \t<li>[latex]50\\%[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h2>Method Two:<\/h2>\r\nTo change a common fraction to an equivalent percent, first write the common fraction as a decimal. Then multiply the decimal by 100% (move the decimal point two places to the <strong>right<\/strong>).\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example A<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<ol>\r\n \t<li>[latex]\\frac{3}{8}=\\text{_____}\\%[\/latex]<\/li>\r\n \t<li>Use long division to write the fraction as a decimal.<\/li>\r\n \t<li>[latex]\\frac{3}{8}=0.375[\/latex]<\/li>\r\n \t<li>Move the decimal two spots to the right.\r\n[latex]\\begin{equation}\\begin{split}&amp;\\curvearrowright \\\\ 0&amp;.375=37.5\\end{split}\\end{equation}[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%;\" border=\"0\"><caption>Convert [latex]\\frac{3}{8}[\/latex] to a percentage<\/caption>\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%;\"><\/td>\r\n<td style=\"width: 25%;\">[latex]\\frac{3}{8} = \\text{_____}\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">Use long division to write fraction as a decimal.<\/td>\r\n<td style=\"width: 25%;\"><img class=\"alignnone wp-image-1264 \" src=\"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.47.44-PM.png\" alt=\"A long division equation showing that 3 divided by 8 equals 0.375.\" width=\"86\" height=\"146\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\"><\/td>\r\n<td style=\"width: 25%;\">[latex]\\frac{3}{8} = 0.375[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">Move the decimal point two places to the right and add the percent sign.<\/td>\r\n<td style=\"width: 25%;\">[latex]0.375 = 37.5\\%[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%; height: 142px;\" border=\"0\"><caption>Convert [latex]\\frac{1}{3}[\/latex] to a percentage<\/caption>\r\n<tbody>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 50%; height: 16px;\"><\/td>\r\n<td style=\"width: 25%; height: 16px;\">[latex]\\frac{1}{3} = \\text{_____}\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 77px;\">\r\n<td style=\"width: 50%; height: 77px;\">Use long division to write fraction as a decimal.<\/td>\r\n<td style=\"width: 25%; height: 77px;\"><img class=\"alignnone wp-image-1265 \" src=\"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.47.51-PM.png\" alt=\"A long division equation showing that 1 divided by 3 equals 0.333 repeating.\" width=\"97\" height=\"78\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 50%; height: 16px;\"><\/td>\r\n<td style=\"width: 25%; height: 16px;\">[latex]\\frac{1}{3} = 0.33\\overline{3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 33px;\">\r\n<td style=\"width: 50%; height: 33px;\">Move the decimal point two places to the right and add the percent sign.<\/td>\r\n<td style=\"width: 25%; height: 33px;\">[latex]0.33\\overline{3}=33.\\overline{3}\\% \\text{ also written as } 33\\frac{1}{3}\\%[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%; height: 64px;\" border=\"0\"><caption>Convert [latex]\\frac{11}{12}[\/latex] to a percentage<\/caption>\r\n<tbody>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 50%; height: 16px;\"><\/td>\r\n<td style=\"width: 25%; height: 16px;\">[latex]\\frac{11}{12} = \\text{_____}\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 50%; height: 16px;\">Use long division to write fraction as a decimal.<\/td>\r\n<td style=\"width: 25%; height: 16px;\"><img class=\"alignnone wp-image-1266 \" src=\"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.47.58-PM.png\" alt=\"A long division equation showing that 11 divided by 12 equals 0.9166 repeating.\" width=\"93\" height=\"177\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 50%; height: 16px;\"><\/td>\r\n<td style=\"width: 25%; height: 16px;\">[latex]\\frac{11}{12} = 0.91\\overline{6}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 50%; height: 16px;\">\u00a0Move the decimal point two places to the right and add the percent sign.<\/td>\r\n<td style=\"width: 25%; height: 16px;\">[latex]0.916\\overline{6} = 91.\\overline{6}\\%[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 7<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<ol type=\"A\">\r\n \t<li>[latex]\\tfrac{1}{12}=0.08\\overline{3} \\ \\ \\ \\ \\ \\ 0.08\\overline{3}\\times100\\%=8.\\overline{3}\\%[\/latex]<\/li>\r\n \t<li>[latex]\\tfrac{1}{8}[\/latex]<\/li>\r\n \t<li>[latex]\\tfrac{5}{8}[\/latex]<\/li>\r\n \t<li>[latex]\\tfrac{7}{8}[\/latex]<\/li>\r\n \t<li>[latex]\\tfrac{2}{3}[\/latex]<\/li>\r\n \t<li>[latex]\\tfrac{5}{16}[\/latex]<\/li>\r\n \t<li>[latex]\\tfrac{5}{6}[\/latex]<\/li>\r\n \t<li>[latex]\\tfrac{4}{9}[\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 7<\/strong>\r\n<ol start=\"2\" type=\"A\">\r\n \t<li>[latex]12.5\\%[\/latex]<\/li>\r\n \t<li>[latex]62.5\\%[\/latex]<\/li>\r\n \t<li>[latex]87.5\\%[\/latex]<\/li>\r\n \t<li>[latex]66.\\overline{6}\\%[\/latex]<\/li>\r\n \t<li>[latex]31.25\\%[\/latex]<\/li>\r\n \t<li>[latex]83.\\overline{3}\\%[\/latex]<\/li>\r\n \t<li>[latex]44.\\overline{4}\\%[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\nThe method you use to change a common fraction to a percent will depend on the numbers you are working with. Choose whichever method seems easier for the situation. You will also memorize many equivalencies as you work with them. But you should definitely memorize:\r\n<ul>\r\n \t<li>[latex]\\tfrac{1}{3}=33\\tfrac{1}{3}\\%[\/latex]<\/li>\r\n \t<li>[latex]\\tfrac{2}{3}=66\\tfrac{2}{3}\\%[\/latex]<\/li>\r\n<\/ul>\r\n<h1>Changing Percents to Common Fractions<\/h1>\r\nYou know that percents are a form of fraction with an unwritten denominator of 100. A % sign is used.\r\n<div class=\"textbox shaded\">To change any percent to a decimal, common fraction, or mixed number, divide by 100 and remove the percent sign.<\/div>\r\n<strong>To change a percent to a common fraction:<\/strong>\r\n<ul>\r\n \t<li>Write the numerals in the percent as the numerator.<\/li>\r\n \t<li>Write 100 as the denominator. (Remember that the line in a fraction can be a divided by sign, so [latex]58\\%=\\tfrac{58}{100}[\/latex] is the same as [latex]58\\div100[\/latex].)<\/li>\r\n \t<li>Remove the % sign.<\/li>\r\n \t<li>Simplify the fraction: [latex]\\tfrac{58}{100}=\\tfrac{29}{50}[\/latex]<\/li>\r\n<\/ul>\r\n&nbsp;\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example A<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nWrite each percent as a common fraction.\r\n\r\n[latex]38\\%=\\dfrac{38}{100}\\div\\left(\\dfrac{2}{2}\\right)= \\dfrac{38 \\div 2}{100 \\div 2} =\\dfrac{19}{50}[\/latex]\r\n\r\n[latex]25\\%=\\dfrac{25}{100}\\div\\left(\\dfrac{25}{25}\\right)= \\dfrac{25\r\n\r\n\\div 25 }{100 \\div 25}=\\dfrac{1}{4}[\/latex]\r\n\r\n[latex]3\\%=\\dfrac{3}{100}[\/latex]\r\n\r\n<\/div>\r\n<\/div>\r\nNote that <strong>percents greater than or equal to 100 become improper fractions<\/strong> which will be rewritten as mixed numbers.\r\n\r\n[latex]110\\%=\\tfrac{110}{100}=1\\tfrac{10}{100}=1\\tfrac{1}{10}[\/latex] <img class=\"alignnone wp-image-1268 \" src=\"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.52.46-PM.png\" alt=\"A long division equation showing that 110 divided by 100 is 1 with 10 remaining.\" width=\"73\" height=\"92\" \/>\r\n\r\n[latex]120\\%=\\tfrac{120}{100}=1\\tfrac{20}{100}=1\\tfrac{1}{5}[\/latex] <img class=\"alignnone wp-image-1269 \" src=\"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.52.53-PM.png\" alt=\"A long division equation showing that 120 divided by 100 is 1 with 20 remaining.\" width=\"72\" height=\"101\" \/>\r\n\r\nRemember 100% is the whole thing. [latex]100\\%=1[\/latex].\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 8<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nChange each percent to a common fraction. Simplify to lowest terms.\r\n<ol type=\"A\">\r\n \t<li>[latex]31\\%=[\/latex]<\/li>\r\n \t<li>[latex]11\\%=[\/latex]<\/li>\r\n \t<li>[latex]2\\%=[\/latex]<\/li>\r\n \t<li>[latex]20\\%=[\/latex]<\/li>\r\n \t<li>[latex]75\\%=[\/latex]<\/li>\r\n \t<li>[latex]100\\%=[\/latex]<\/li>\r\n \t<li>[latex]750\\%=[\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 8<\/strong>\r\n<ol type=\"A\">\r\n \t<li>[latex]\\tfrac{31}{100}[\/latex]<\/li>\r\n \t<li>[latex]\\tfrac{11}{100}[\/latex]<\/li>\r\n \t<li>[latex]\\tfrac{1}{50}[\/latex]<\/li>\r\n \t<li>[latex]\\tfrac{1}{5}[\/latex]<\/li>\r\n \t<li>[latex]\\tfrac{3}{4}[\/latex]<\/li>\r\n \t<li>[latex]1[\/latex]<\/li>\r\n \t<li>[latex]7\\tfrac{1}{2}[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n<h1>Percents Less Than 1%<\/h1>\r\nSometimes a percent <strong>smaller than 1%<\/strong> is used. For example, you will hear amounts such as [latex]\\tfrac{1}{4}\\%[\/latex] or [latex]\\tfrac{1}{8}\\%[\/latex] or [latex]\\tfrac{1}{2}\\%[\/latex] on the news about the Bank of Canada rate and the rise and fall of inflation. These are small amounts. Sometimes the expression \u201c[latex]\\tfrac{1}{2}\\text{ of a percentage point}[\/latex]\u201d is used instead of \u201c[latex]\\tfrac{1}{2}\\%[\/latex]\u201d.\r\n\r\n&nbsp;\r\n\r\n<strong>What is [latex]\\tfrac{1}{4}\\%[\/latex]?<\/strong>\r\n\r\n[latex]\\tfrac{1}{4}\\%[\/latex] is [latex]\\tfrac{1}{4}\\text{ of }1\\%[\/latex]\r\n\r\n[latex]1\\%=\\tfrac{1}{100}[\/latex], so [latex]\\tfrac{1}{4}\\text{ of }1\\%=\\tfrac{1}{4}\\times\\tfrac{1}{100}=\\tfrac{1}{400}[\/latex]\r\n\r\n[latex]\\tfrac{1}{4}\\%=0.25\\%=0.0025[\/latex]\r\n\r\n&nbsp;\r\n\r\n<strong>What is [latex]\\tfrac{1}{2}\\%[\/latex]?<\/strong>\r\n\r\n[latex]\\tfrac{1}{2}\\%=\\tfrac{1}{2}\\text{ of }1\\%=\\tfrac{1}{2}\\times\\tfrac{1}{100}=\\tfrac{1}{200}[\/latex]\r\n\r\n[latex]\\tfrac{1}{2}\\%=0.5\\%=0.005[\/latex]\r\nTo work with percents less than 1%, change the percent to a decimal by dividing by 100 (move decimal point two places to the left).\r\n\r\n[latex]0.2\\%=0.002[\/latex]\r\n[latex]0.75\\%=0.0075[\/latex]\r\n<div class=\"textbox shaded\">\r\n\r\n<strong>If the percent is expressed as a common fraction, do this:<\/strong>\r\n<ul>\r\n \t<li>Write the common fraction percent as a decimal percent.<\/li>\r\n \t<li>Divide by 100 (move decimal point two places left).<\/li>\r\n<\/ul>\r\n[latex]\\begin{equation}\\begin{split}\r\n\\tfrac{1}{2}\\% &amp;= 0.5\\% &amp;= 0.005 \\\\\r\n\\tfrac{1}{4}\\% &amp;= 0.0025\\% &amp;= 0.0025 \\\\\r\n\\tfrac{1}{8}\\% &amp;= 0.00125\\% &amp;= 0.00125\r\n\\end{split}\\end{equation}[\/latex]\r\n\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 9<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nChange each percent to an equivalent decimal.\r\n<ol type=\"A\">\r\n \t<li>[latex]\\tfrac{1}{2}\\%= [\/latex]<\/li>\r\n \t<li>[latex]0.6\\%= [\/latex]<\/li>\r\n \t<li>[latex]\\tfrac{3}{10}\\%= [\/latex]<\/li>\r\n \t<li>[latex]\\tfrac{3}{5}\\%= [\/latex]<\/li>\r\n \t<li>[latex]0.75\\%= [\/latex]<\/li>\r\n \t<li>[latex]\\tfrac{3}{4}\\%= [\/latex]<\/li>\r\n \t<li>[latex]0.5\\%= [\/latex]<\/li>\r\n \t<li>[latex]\\tfrac{1}{4}\\%= [\/latex]<\/li>\r\n \t<li>[latex]0.125\\%= [\/latex]<\/li>\r\n \t<li>[latex]\\tfrac{5}{8}\\%= [\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 9<\/strong>\r\n<ol type=\"A\">\r\n \t<li>[latex]0.005[\/latex]<\/li>\r\n \t<li>[latex]0.006[\/latex]<\/li>\r\n \t<li>[latex]0.003[\/latex]<\/li>\r\n \t<li>[latex]0.006[\/latex]<\/li>\r\n \t<li>[latex]0.0075[\/latex]<\/li>\r\n \t<li>[latex]0.0075[\/latex]<\/li>\r\n \t<li>[latex]0.005[\/latex]<\/li>\r\n \t<li>[latex]0.0025[\/latex]<\/li>\r\n \t<li>[latex]0.00125[\/latex]<\/li>\r\n \t<li>[latex]0.00625[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n<h1>16\u2154%, 33\u2153%, 66\u2154%, 83\u2153% ...<\/h1>\r\nThese percents will become repeating decimals. For example:\r\n\r\n[latex]\\begin{equation}\\begin{split}\r\n33\\tfrac{1}{3}\\% &amp;= 33.\\overline{3}\\% &amp;= 0.33\\overline{3} \\\\\r\n\\\\\r\n66\\tfrac{2}{3}\\% &amp;= 66.\\overline{6}\\% &amp;= 0.66\\overline{6}\r\n\\end{split}\\end{equation}[\/latex]\r\n\r\nIt is usually more convenient to use the common fraction equivalent of these percents. Memorize them, or make a note on a special paper and post it near your work space.\r\n\r\n[latex]\\begin{equation}\\begin{split}\r\n33\\tfrac{1}{3}\\% &amp;= 33\\tfrac{1}{3}\\div100 &amp;= \\tfrac{100}{3}\\times\\tfrac{1}{100} \\ &amp;= \\tfrac{1}{3} \\\\\r\n\\\\\r\n66\\tfrac{2}{3}\\% &amp;= 66\\tfrac{2}{3}\\div100 &amp;= \\tfrac{200}{3}\\times\\tfrac{1}{100} \\ &amp;= \\tfrac{2}{3}\r\n\\end{split}\\end{equation}[\/latex]\r\n<div class=\"textbox shaded\">[latex]\\begin{equation}\\begin{split}\r\n16\\tfrac{2}{3}\\% &amp;= \\tfrac{1}{6} \\\\\r\n\\\\\r\n33\\tfrac{1}{3}\\% &amp;= \\tfrac{1}{3} \\\\\r\n\\\\\r\n66\\tfrac{2}{3}\\% &amp;= \\tfrac{2}{3} \\\\\r\n\\\\\r\n83\\tfrac{1}{3}\\% &amp;= \\tfrac{5}{6}\r\n\\end{split}\\end{equation}[\/latex]<\/div>\r\n&nbsp;\r\n<h1>Review of Equivalent Common Fractions, Decimals, and Percents<\/h1>\r\nComplete this chart. These are equivalents that you will often use, so use this chart for reference. Memorize as many equivalents as you can. You may wish to put other equivalents on the chart.\r\n<table style=\"border-collapse: collapse; width: 100%;\">\r\n<tbody>\r\n<tr>\r\n<th style=\"width: 33.3%; text-align: center;\" scope=\"col\">Common Fraction<\/th>\r\n<th style=\"width: 33.3%; text-align: center; vertical-align: top;\" scope=\"col\">Decimal<\/th>\r\n<th style=\"width: 33.3%; text-align: center; vertical-align: top;\" scope=\"col\">Percent<\/th>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]\\tfrac{1}{4}[\/latex]<\/td>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\"><\/td>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\"><\/td>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]0.5[\/latex]<\/td>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\"><\/td>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\"><\/td>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]75\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]\\tfrac{1}{8}[\/latex]<\/td>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\"><\/td>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\"><\/td>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]0.375[\/latex]<\/td>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\"><\/td>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\"><\/td>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]62.5\\%[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"textbox shaded\">\r\n\r\n<strong>Answers to Review of Equivalent Common Fractions, Decimals, and Percents<\/strong>\r\n<table style=\"border-collapse: collapse; width: 100%;\">\r\n<tbody>\r\n<tr>\r\n<th style=\"width: 33.3%; text-align: center;\" scope=\"col\">Common Fraction<\/th>\r\n<th style=\"width: 33.3%; text-align: center; vertical-align: top;\" scope=\"col\">Decimal<\/th>\r\n<th style=\"width: 33.3%; text-align: center; vertical-align: top;\" scope=\"col\">Percent<\/th>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]\\tfrac{1}{4}[\/latex]<\/td>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]0.25[\/latex]<\/td>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]25\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]\\tfrac{1}{2}[\/latex]<\/td>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]0.5[\/latex]<\/td>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]50\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]\\tfrac{3}{4}[\/latex]<\/td>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]0.75[\/latex]<\/td>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]75\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]\\tfrac{1}{8}[\/latex]<\/td>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]0.125[\/latex]<\/td>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]12.5\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]\\tfrac{3}{8}[\/latex]<\/td>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]0.375[\/latex]<\/td>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]37.5\\%[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]\\tfrac{5}{8}[\/latex]<\/td>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]0.625[\/latex]<\/td>\r\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]62.5\\%[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n<h1>Topic A: Self-Test<\/h1>\r\n<strong>Mark\u00a0 \u00a0 \u00a0 \u00a0\/15\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Aim\u00a0 \u00a0 \u00a0 \u00a0 13\/15<\/strong>\r\n<ol type=\"A\">\r\n \t<li>Write these percents in numeral form.\r\n<strong>(2 marks)<\/strong>\r\n<ol type=\"i\">\r\n \t<li>Sixty-two and one-half percent<\/li>\r\n \t<li>One hundred six and one-fifth percent<\/li>\r\n<\/ol>\r\n&nbsp;<\/li>\r\n \t<li>Write these percents in words.\r\n<strong>(2 marks)<\/strong>\r\n<ol type=\"i\">\r\n \t<li>[latex]72\\%[\/latex]<\/li>\r\n \t<li>[latex]\\tfrac{3}{4}\\%[\/latex]<\/li>\r\n<\/ol>\r\n&nbsp;<\/li>\r\n \t<li>Change the percents to decimal fractions.\r\n<strong>(5 marks)<\/strong>\r\n<ol type=\"i\">\r\n \t<li>[latex]32\\%[\/latex]<\/li>\r\n \t<li>[latex]18.5\\%[\/latex]<\/li>\r\n \t<li>[latex]125\\%[\/latex]<\/li>\r\n \t<li>[latex]\\tfrac{4}{5}\\%[\/latex]<\/li>\r\n \t<li>[latex]\\tfrac{2}{3}\\%[\/latex]<\/li>\r\n<\/ol>\r\n&nbsp;<\/li>\r\n \t<li>Change these percents to common fractions in lowest terms.\r\n<strong>(4 marks)<\/strong>\r\n<ol type=\"i\">\r\n \t<li>[latex]16\\%[\/latex]<\/li>\r\n \t<li>[latex]20\\%[\/latex]<\/li>\r\n \t<li>[latex]106\\%[\/latex]<\/li>\r\n \t<li>[latex]75\\%[\/latex]<\/li>\r\n<\/ol>\r\n&nbsp;<\/li>\r\n \t<li>Change these common fractions to equivalent percents.\r\n<strong>(2 marks)<\/strong>\r\n<ol type=\"i\">\r\n \t<li>[latex]\\tfrac{4}{5}[\/latex]<\/li>\r\n \t<li>[latex]\\tfrac{3}{8}[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n&nbsp;\r\n<div class=\"textbox shaded\">\r\n\r\n<strong>Answers to Topic A Self-Test<\/strong>\r\n<ol type=\"A\">\r\n \t<li style=\"list-style-type: none;\">\r\n<ol type=\"i\">\r\n \t<li>[latex]62.5\\%[\/latex] or [latex]62\\tfrac{1}{2}\\%[\/latex]<\/li>\r\n \t<li>[latex]106.2\\%[\/latex] or [latex]106\\tfrac{1}{5}\\%[\/latex]<\/li>\r\n<\/ol>\r\n<ol type=\"i\">\r\n \t<li>Seventy-two percent<\/li>\r\n \t<li>Three-quarters percent<\/li>\r\n<\/ol>\r\n<ol type=\"i\">\r\n \t<li>[latex]0.32[\/latex]<\/li>\r\n \t<li>[latex]0.185[\/latex]<\/li>\r\n \t<li>[latex]1.25[\/latex]<\/li>\r\n \t<li>[latex]0.008[\/latex]<\/li>\r\n \t<li>[latex]0.00\\overline{6}[\/latex]<\/li>\r\n<\/ol>\r\n<ol type=\"i\">\r\n \t<li>[latex]\\tfrac{4}{25}[\/latex]<\/li>\r\n \t<li>[latex]\\tfrac{1}{5}[\/latex]<\/li>\r\n \t<li>[latex]1\\tfrac{3}{50}[\/latex]<\/li>\r\n \t<li>[latex]\\tfrac{3}{4}[\/latex]<\/li>\r\n<\/ol>\r\n<ol type=\"i\">\r\n \t<li>[latex]80\\%[\/latex]<\/li>\r\n \t<li>[latex]37.5\\%[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<\/div>","rendered":"<h1>Reading and Writing Percents<\/h1>\n<p><strong>To write a percent:<\/strong><\/p>\n<ul>\n<li>Write the number in the usual way<\/li>\n<li>Place the percent sign after the numerals\n<ul>\n<li>[latex]50\\%[\/latex]<\/li>\n<li>[latex]5\\frac{1}{2}\\%[\/latex] or [latex]5.5\\%[\/latex]<\/li>\n<li>[latex]\\frac{3}{4}\\%[\/latex] or [latex]0.75\\%[\/latex]<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><strong>To read a percent:<\/strong><\/p>\n<ul>\n<li>Read the numbers in the usual way<\/li>\n<li>Say \u201cpercent&#8221; after the number\n<ul>\n<li>[latex]16\\%[\/latex]: say \u201csixteen percent&#8221;<\/li>\n<li>[latex]4\\frac{1}{2}\\%[\/latex]: say &#8220;four and one-half percent&#8221;<\/li>\n<li>[latex]0.25\\%[\/latex]: say &#8220;twenty-five hundredths percent,&#8221; or \u201cone-quarter percent,&#8221; or \u201cpoint two five percent&#8221;<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Write these percents using numerals and a percent sign. Note that the mixed numbers may be expressed with common fractions or decimals.<\/p>\n<ol type=\"A\">\n<li>Thirty-four percent <span aria-label=\"blank;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>[latex]34\\%[\/latex]<\/li>\n<li>Twelve percent<\/li>\n<li>Four-fifths percent<\/li>\n<li>One hundred sixteen and three-tenths percent<\/li>\n<li>Thirteen percent<\/li>\n<li>Six and one-fifth percent<\/li>\n<li>Ninety-four and one-half percent<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 1<\/strong><\/p>\n<ol start=\"2\" type=\"A\">\n<li>[latex]12\\%[\/latex]<\/li>\n<li>[latex]0.8\\%[\/latex] or [latex]\\frac{4}{5}\\%[\/latex]<\/li>\n<li>[latex]116.3\\%[\/latex] or [latex]116\\frac{3}{10}\\%[\/latex]<\/li>\n<li>[latex]13\\%[\/latex]<\/li>\n<li>[latex]6.2\\%[\/latex] or [latex]6\\frac{1}{5}\\%[\/latex]<\/li>\n<li>[latex]94.5\\%[\/latex] or [latex]94\\frac{1}{2}\\%[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol type=\"A\">\n<li>[latex]62\\%[\/latex] <span aria-label=\"blank;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span><span aria-label=\"blank;\">sixty-two percent<\/span><\/li>\n<li>[latex]37\\frac{1}{2}\\%[\/latex]<\/li>\n<li>[latex]202\\%[\/latex]<\/li>\n<li>[latex]\\frac{3}{4}\\%[\/latex]<\/li>\n<li>[latex]18.3\\%[\/latex]<\/li>\n<li>[latex]14\\frac{1}{2}\\%[\/latex]<\/li>\n<li>[latex]100\\frac{1}{2}\\%[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 2<\/strong><\/p>\n<ol start=\"2\" type=\"A\">\n<li>Thirty-seven and one-half percent<\/li>\n<li>Two hundred two percent<\/li>\n<li>Three-quarters percent<\/li>\n<li>Eighteen and three-tenths percent<\/li>\n<li>Five-tenths percent or one-half percent or zero point five percent<\/li>\n<li>One hundred percent<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1>Changing Decimals to Percents<\/h1>\n<p>Writing equivalent fractions is an important math skill.<\/p>\n<p>Equivalent common fractions, decimals, and percents all represent the same amount.<\/p>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%; height: 48px;\">\n<caption>Equivalent fractions, decimals, and percentages<\/caption>\n<tbody>\n<tr style=\"height: 16px;\">\n<th style=\"width: 33.3333%; height: 16px;\" scope=\"col\">Fractions<\/th>\n<th style=\"width: 33.3333%; height: 16px;\" scope=\"col\">Decimals<\/th>\n<th style=\"width: 33.3333%; height: 16px;\" scope=\"col\">Percentages<\/th>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">[latex]\\frac{1}{2}[\/latex]<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">[latex]0.5[\/latex]<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">[latex]50\\%[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">[latex]\\frac{3}{10}[\/latex]<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">[latex]0.3[\/latex]<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">[latex]30\\%[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>You need the skill of writing equivalent fractions for working with percents.<\/p>\n<div class=\"textbox shaded\">To change any number to a percent, multiply the number by 100% and place a percent sign % after the product.<\/div>\n<p>&nbsp;<\/p>\n<p>Remember this shortcut for multiplying by 100?<\/p>\n<p style=\"text-align: center;\">[latex]4.27\\times100=427[\/latex]<br \/>\n[latex]0.287\\times100=28.7[\/latex]<br \/>\n[latex]53\\times100=5300[\/latex]<\/p>\n<p>The shortcut is: <strong>When multiplying by 100, move the decimal point two places to the right.<\/strong><\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example A<\/p>\n<\/header>\n<div class=\"textbox__content\">Change these numbers to a percent.[latex]\\begin{equation}\\begin{split}  &1 \\ \\ \\ \\ \\ \\ \\ \\ &1\\times100\\% \\ \\ \\ \\ &= \\ \\ \\ \\ &100\\% \\\\  &0.25 \\ \\ \\ \\ \\ \\ \\ &0.25\\times100\\% \\ \\ \\ \\ &= \\ \\ \\ \\ &25\\% \\\\  &0.8 \\ \\ \\ \\ \\ \\ \\ &0.8\\times100\\% \\ \\ \\ \\ &= \\ \\ \\ \\ &80\\% \\\\  &0.375 \\ \\ \\ \\ \\ \\ \\ &0.375\\times100\\% \\ \\ \\ \\ &= \\ \\ \\ \\ &37.5\\% \\\\  \\end{split}\\end{equation}[\/latex]<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>So&#8230;<\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox shaded\">To change a decimal to a percent, move the decimal point two places to the right and then write the percent sign after the number.<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example B<\/p>\n<\/header>\n<div class=\"textbox__content\">Change each decimal to a percent.<\/div>\n<div class=\"textbox__content\">[latex]\\begin{equation}\\begin{split}  &\\curvearrowright \\\\  0.125=0&.125=12.5\\%  \\end{split}\\end{equation}[\/latex]<\/div>\n<div class=\"textbox__content\">[latex]\\begin{equation}\\begin{split}  &\\curvearrowright \\\\  1.375=1&.375=137.5\\%  \\end{split}\\end{equation}[\/latex]<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>If the decimal point moves to the end of the number it is not necessary to write the decimal point. Remember that zeros at the beginning of a number are also not necessary.<\/p>\n<p>[latex]\\begin{equation}\\begin{split}  &\\curvearrowright \\\\  0.24=0&.24=\\cancel{0}.24\\%=24\\%  \\end{split}\\end{equation}[\/latex]<\/p>\n<p>[latex]\\begin{equation}\\begin{split}  &\\curvearrowright \\\\  0.05=0&.05=\\cancel{0.0}5\\%=5\\%  \\end{split}\\end{equation}[\/latex]<\/p>\n<p>If the decimal is a tenth (one decimal place), it will be necessary to add a zero. If you are changing a whole number to a percent, add two zeros.<\/p>\n<p>[latex]\\begin{equation}\\begin{split}  &\\curvearrowright \\\\  0.4=0&.40=40\\%  \\end{split}\\end{equation}[\/latex]<\/p>\n<p>[latex]\\begin{equation}\\begin{split}  &\\curvearrowright \\\\  1.7=1&.70=170\\%  \\end{split}\\end{equation}[\/latex]<\/p>\n<p>[latex]\\begin{equation}\\begin{split}  &\\curvearrowright \\\\  2=2&.00=200\\%  \\end{split}\\end{equation}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Change these decimals to percents.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<th style=\"width: 15%; text-align: center;\" scope=\"col\"><\/th>\n<th style=\"width: 25%; text-align: center; vertical-align: top;\" scope=\"col\">Decimal<\/th>\n<th style=\"width: 35%; text-align: center; vertical-align: top;\" scope=\"col\">\u00d7 100%<br \/>\nMove decimal 2 places to right<\/th>\n<th style=\"width: 25%; text-align: center; vertical-align: top;\" scope=\"col\">= Percent<\/th>\n<\/tr>\n<tr>\n<th style=\"width: 15%; text-align: center;\" scope=\"row\">A.<\/th>\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]0.75[\/latex]<\/td>\n<td style=\"width: 35%; text-align: center;\" scope=\"col\">[latex]\\begin{equation}\\begin{split}  &\\curvearrowright \\\\  0&.75  \\end{split}\\end{equation}[\/latex]<\/td>\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]=75\\%[\/latex]<\/td>\n<\/tr>\n<tr>\n<th style=\"width: 15%; text-align: center;\" scope=\"row\">B.<\/th>\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]0.33[\/latex]<\/td>\n<td style=\"width: 35%; text-align: center;\" scope=\"col\"><\/td>\n<td style=\"width: 25%; text-align: center;\" scope=\"col\"><\/td>\n<\/tr>\n<tr>\n<th style=\"width: 15%; text-align: center;\" scope=\"row\">C.<\/th>\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]0.1[\/latex]<\/td>\n<td style=\"width: 35%; text-align: center;\" scope=\"col\"><\/td>\n<td style=\"width: 25%; text-align: center;\" scope=\"col\"><\/td>\n<\/tr>\n<tr>\n<th style=\"width: 15%; text-align: center;\" scope=\"row\">D.<\/th>\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]0.0025[\/latex]<\/td>\n<td style=\"width: 35%; text-align: center;\" scope=\"col\"><\/td>\n<td style=\"width: 25%; text-align: center;\" scope=\"col\"><\/td>\n<\/tr>\n<tr>\n<th style=\"width: 15%; text-align: center;\" scope=\"row\">E.<\/th>\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]0.9[\/latex]<\/td>\n<td style=\"width: 35%; text-align: center;\" scope=\"col\"><\/td>\n<td style=\"width: 25%; text-align: center;\" scope=\"col\"><\/td>\n<\/tr>\n<tr>\n<th style=\"width: 15%; text-align: center;\" scope=\"row\">F.<\/th>\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]0.325[\/latex]<\/td>\n<td style=\"width: 35%; text-align: center;\" scope=\"col\"><\/td>\n<td style=\"width: 25%; text-align: center;\" scope=\"col\"><\/td>\n<\/tr>\n<tr>\n<th style=\"width: 15%; text-align: center;\" scope=\"row\">G.<\/th>\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]0.0625[\/latex]<\/td>\n<td style=\"width: 35%; text-align: center;\" scope=\"col\"><\/td>\n<td style=\"width: 25%; text-align: center;\" scope=\"col\"><\/td>\n<\/tr>\n<tr>\n<th style=\"width: 15%; text-align: center;\" scope=\"row\">H.<\/th>\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]3[\/latex]<\/td>\n<td style=\"width: 35%; text-align: center;\" scope=\"col\"><\/td>\n<td style=\"width: 25%; text-align: center;\" scope=\"col\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>Answers to Exercise 3<\/strong><\/p>\n<ol start=\"2\" type=\"A\">\n<li>[latex]33\\%[\/latex]<\/li>\n<li>[latex]10\\%[\/latex]<\/li>\n<li>[latex]0.25\\%[\/latex]<\/li>\n<li>[latex]90\\%[\/latex]<\/li>\n<li>[latex]32.5\\%[\/latex]<\/li>\n<li>[latex]6.25\\%[\/latex]<\/li>\n<li>[latex]300\\%[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<h1>Changing Percents to Decimals<\/h1>\n<p>Review dividing by 100:<\/p>\n<p style=\"text-align: center;\">[latex]47.39\\div100=0.4739[\/latex]<br \/>\n[latex]429\\div100=4.29[\/latex]<br \/>\n[latex]3.824\\div100=0.03824[\/latex]<\/p>\n<p><strong>To divide by 100, move the decimal point two places to the left.<\/strong><\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example A<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Change each percent to a decimal or mixed number.<\/p>\n<p>[latex]\\begin{equation}\\begin{split}  58\\% \\ \\ &= \\ \\ 58\\div100 \\ \\ &= \\ \\ .58 \\ \\ &= \\ \\ 0.58 \\\\  20\\% \\ \\ &= \\ \\ 20\\div100 \\ \\ &= \\ \\ .2 \\ \\ &= \\ \\ 0.2 \\\\  6\\% \\ \\ &= \\ \\ 6\\div100 \\ \\ &= \\ \\ .06 \\ \\ &= \\ \\ 0.06 \\\\  110\\% \\ \\ &= \\ \\ 110\\div100 \\ \\ &= \\ \\ 1.10  \\end{split}\\end{equation}[\/latex]<\/p>\n<\/div>\n<\/div>\n<p>So&#8230;<\/p>\n<div class=\"textbox shaded\">To change a percent to a decimal, divide by 100 (move the decimal point two places to the <strong>left<\/strong>) and remove the percent sign.<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example B<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Change each percent to a decimal.<\/p>\n<p>[latex]\\begin{equation}\\begin{split}  75\\% \\ \\ &= \\ \\ 75.0\\% \\ \\ &= \\ \\ 0.75 \\\\  12\\% \\ \\ &= \\ \\ 12.0\\% \\ \\ &= \\ \\ 0.12 \\\\  37.5\\% \\ \\ &= \\ \\ 37.5\\% \\ \\ &= \\ \\ 0.375 \\\\  125\\% \\ \\ &= \\ \\ 125.0\\% \\ \\ &= \\ \\ 1.25 \\\\  5\\% \\ \\ &= \\ \\ 5.0\\% \\ \\ &= \\ \\ 0.05 \\\\  4.6\\% \\ \\ &= \\ \\ 4.6\\% \\ \\ &= \\ \\ 0.046 \\\\  \\end{split}\\end{equation}[\/latex]<\/p>\n<\/div>\n<\/div>\n<p>Some notes to remember:<\/p>\n<ul>\n<li>If there is no decimal point in the percent, place the decimal point <strong>after<\/strong> the last numeral and <strong>then<\/strong> divide by 100.[latex]24\\%=24.0\\%=0.24[\/latex]<\/li>\n<li>It may be necessary to <strong>prefix<\/strong> zeros. (This means adding zeros in front of the number, if needed).[latex]6\\%=6.0\\%=0.06[\/latex]<\/li>\n<li>A zero at the right of a decimal is not needed and may be left off.[latex]40\\%=40.0\\%=0.40=0.4[\/latex]<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Change each percent to its decimal equivalent.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<th style=\"width: 15%; text-align: center;\" scope=\"col\"><\/th>\n<th style=\"width: 25%; text-align: center; vertical-align: top;\" scope=\"col\">Percent<\/th>\n<th style=\"width: 35%; text-align: center; vertical-align: top;\" scope=\"col\">\u00f7 100%<br \/>\nMove decimal 2 places to left<\/th>\n<th style=\"width: 25%; text-align: center; vertical-align: top;\" scope=\"col\">= Decimal<\/th>\n<\/tr>\n<tr>\n<th style=\"width: 15%; text-align: center;\" scope=\"row\">A.<\/th>\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]23\\%[\/latex]<\/td>\n<td style=\"width: 35%; text-align: center;\" scope=\"col\">[latex]\\begin{equation}\\begin{split}  &\\curvearrowleft \\\\  & \\ 23.  \\end{split}\\end{equation}[\/latex]<\/td>\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]=0.23[\/latex]<\/td>\n<\/tr>\n<tr>\n<th style=\"width: 15%; text-align: center;\" scope=\"row\">B.<\/th>\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]1\\%[\/latex]<\/td>\n<td style=\"width: 35%; text-align: center;\" scope=\"col\"><\/td>\n<td style=\"width: 25%; text-align: center;\" scope=\"col\"><\/td>\n<\/tr>\n<tr>\n<th style=\"width: 15%; text-align: center;\" scope=\"row\">C.<\/th>\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]112\\%[\/latex]<\/td>\n<td style=\"width: 35%; text-align: center;\" scope=\"col\"><\/td>\n<td style=\"width: 25%; text-align: center;\" scope=\"col\"><\/td>\n<\/tr>\n<tr>\n<th style=\"width: 15%; text-align: center;\" scope=\"row\">D.<\/th>\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]10.3\\%[\/latex]<\/td>\n<td style=\"width: 35%; text-align: center;\" scope=\"col\"><\/td>\n<td style=\"width: 25%; text-align: center;\" scope=\"col\"><\/td>\n<\/tr>\n<tr>\n<th style=\"width: 15%; text-align: center;\" scope=\"row\">E.<\/th>\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]36\\%[\/latex]<\/td>\n<td style=\"width: 35%; text-align: center;\" scope=\"col\"><\/td>\n<td style=\"width: 25%; text-align: center;\" scope=\"col\"><\/td>\n<\/tr>\n<tr>\n<th style=\"width: 15%; text-align: center;\" scope=\"row\">F.<\/th>\n<td style=\"width: 25%; text-align: center;\" scope=\"col\">[latex]147\\%[\/latex]<\/td>\n<td style=\"width: 35%; text-align: center;\" scope=\"col\"><\/td>\n<td style=\"width: 25%; text-align: center;\" scope=\"col\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>Answers to Exercise 4<\/strong><\/p>\n<ol start=\"2\" type=\"A\">\n<li>[latex]0.01[\/latex]<\/li>\n<li>[latex]1.12[\/latex]<\/li>\n<li>[latex]0.103[\/latex]<\/li>\n<li>[latex]0.36[\/latex]<\/li>\n<li>[latex]1.47[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p><strong>To change a percent containing a common fraction to a decimal<\/strong>, do this:<\/p>\n<ul>\n<li>Change the common fraction in the percent to a decimal in the percent.<\/li>\n<li>Divide by 100 (move the decimal 2 places to the <strong>left<\/strong>).<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example C<\/p>\n<\/header>\n<div class=\"textbox__content\">[latex]\\begin{equation}\\begin{split}  3\\tfrac{1}{2}\\% \\ \\ &= \\ \\ 3.5\\% \\ \\ \\ \\ \\ \\ \\ &3.5\\% &\\div 100 \\ &= .035 &= 0.035 \\\\  37\\tfrac{1}{2}\\% \\ \\ &= \\ \\ 37.5\\% \\ \\ \\ \\ \\ \\ \\ &37.5\\% &\\div 100 \\ &= .375 &= 0.375 \\\\  \\tfrac{1}{4}\\% \\ \\ &= \\ \\ 0.25\\% \\ \\ \\ \\ \\ \\ \\ &0.25\\% &\\div 100 \\ &= .0025 \\\\  17\\tfrac{1}{3}\\% \\ \\ &= \\ \\ 17.\\overline{3}\\% \\ \\ \\ \\ \\ \\ \\ &17.\\overline{3}\\% &\\div 100 \\ &= 0.17\\overline{3}  \\end{split}\\end{equation}[\/latex]<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Change each percent to its decimal equivalent.<\/p>\n<ol type=\"A\">\n<li>[latex]8\\frac{4}{5}\\%= \\ \\ \\ \\ \\ 8.8\\%=0.088[\/latex]<\/li>\n<li>[latex]4\\frac{1}{2}\\%=[\/latex]<\/li>\n<li>[latex]56\\frac{3}{4}\\%=[\/latex]<\/li>\n<li>[latex]1\\frac{3}{5}\\%=[\/latex]<\/li>\n<li>[latex]112\\frac{1}{2}\\%=[\/latex]<\/li>\n<li>[latex]2\\frac{3}{8}\\%=[\/latex]<\/li>\n<li>[latex]5\\frac{1}{4}\\%=[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 5<\/strong><\/p>\n<ol start=\"2\" type=\"A\">\n<li>[latex]0.045[\/latex]<\/li>\n<li>[latex]0.5675[\/latex]<\/li>\n<li>[latex]0.016[\/latex]<\/li>\n<li>[latex]1.125[\/latex]<\/li>\n<li>[latex]0.02375[\/latex]<\/li>\n<li>[latex]0.0525[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<h1>Changing Common Fractions to Percents<\/h1>\n<div class=\"textbox shaded\">To change any number to a percent, multiply the number by 100% and place the percent sign % after the product.<\/div>\n<p>There are two methods you can use to change a common fraction to a percent.<\/p>\n<h2>Method One:<\/h2>\n<p>To change a common fraction to an equivalent percent, <strong>multiply the common fraction by 100%.<\/strong><\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example A<\/p>\n<\/header>\n<div class=\"textbox__content\">[latex]\\frac{3}{4} = \\text{_____}\\%[\/latex]<\/div>\n<div class=\"textbox__content\">\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%; height: 147px;\">\n<tbody>\n<tr>\n<td style=\"width: 36.8881%;\"><\/td>\n<td style=\"width: 38.1119%; height: 16px;\">[latex]\\frac{3}{4}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 36.8881%;\">Multiply by 100%<\/td>\n<td style=\"width: 38.1119%; height: 33px;\">[latex]\\frac{3}{4} \\times 100\\%[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 36.8881%;\">Convert 100% to a fraction.<\/td>\n<td style=\"width: 38.1119%; height: 33px;\">[latex]\\frac{3}{4} \\times \\frac{100}{1}\\%[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 36.8881%;\">Simplify the fractions by dividing the numerator and denominator by 4.<\/td>\n<td style=\"width: 38.1119%;\">[latex]\\frac{3}{\\cancel{4}1} \\times \\frac{\\cancel{100}25}{1}\\%[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 36.8881%;\">The 4 cancels and 100 is reduced to 25.<\/td>\n<td style=\"width: 38.1119%; height: 33px;\">[latex]\\frac{3}{1} \\times \\frac{25}{1}\\%[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 36.8881%;\">Multiply 3 by 25%.<\/td>\n<td style=\"width: 38.1119%; height: 16px;\">[latex]3 \\times 25\\%[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 36.8881%;\"><\/td>\n<td style=\"width: 38.1119%; height: 16px;\">[latex]75\\%[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div><\/div>\n<div class=\"textbox__content\">[latex]1\\frac{1}{5} = \\text{_____}\\%[\/latex]<\/div>\n<div class=\"textbox__content\">\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 36.7133%;\"><\/td>\n<td style=\"width: 38.2867%;\">[latex]1\\frac{1}{5}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 36.7133%;\">Convert number to a fraction.<\/td>\n<td style=\"width: 38.2867%;\">[latex]\\frac{6}{5}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 36.7133%;\">Multiply by 100%.<\/td>\n<td style=\"width: 38.2867%;\">[latex]\\frac{6}{5} \\times 100\\%[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 36.7133%;\">Convert 100% to a fraction.<\/td>\n<td style=\"width: 38.2867%;\">[latex]\\frac{6}{5} \\times \\frac{100}{1}\\%[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 36.7133%;\">Simplify the fractions by dividing the denominator and numerator by 5.<\/td>\n<td style=\"width: 38.2867%;\">[latex]\\frac{6}{\\cancel{5}1} \\times \\frac{\\cancel{100}20}{1}\\%[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 36.7133%;\">The 5 cancels and 100 is reduced to 20.<\/td>\n<td style=\"width: 38.2867%;\">[latex]\\frac{6}{1} \\times \\frac{20}{1}\\%[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 36.7133%;\">Multiply 6 by 20%.<\/td>\n<td style=\"width: 38.2867%;\">[latex]6 \\times 20\\%[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 36.7133%;\"><\/td>\n<td style=\"width: 38.2867%;\">[latex]120\\%[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Multiply by 100% to change each common fraction to an equivalent percent.<\/p>\n<ol type=\"A\">\n<li>[latex]\\frac{4}{5} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\frac{4}{5}\\times100\\%=80\\%[\/latex]<\/li>\n<li>[latex]\\frac{1}{5}\\%=[\/latex]<\/li>\n<li>[latex]\\frac{9}{10}\\%=[\/latex]<\/li>\n<li>[latex]1\\frac{1}{2}\\%=[\/latex]<\/li>\n<li>[latex]\\frac{7}{10}\\%=[\/latex]<\/li>\n<li>[latex]3\\frac{3}{4}\\%=[\/latex]<\/li>\n<li>[latex]\\frac{1}{2}\\%=[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 6<\/strong><\/p>\n<ol start=\"2\" type=\"A\">\n<li>[latex]20\\%[\/latex]<\/li>\n<li>[latex]90\\%[\/latex]<\/li>\n<li>[latex]150\\%[\/latex]<\/li>\n<li>[latex]70\\%[\/latex]<\/li>\n<li>[latex]375\\%[\/latex]<\/li>\n<li>[latex]50\\%[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h2>Method Two:<\/h2>\n<p>To change a common fraction to an equivalent percent, first write the common fraction as a decimal. Then multiply the decimal by 100% (move the decimal point two places to the <strong>right<\/strong>).<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example A<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol>\n<li>[latex]\\frac{3}{8}=\\text{_____}\\%[\/latex]<\/li>\n<li>Use long division to write the fraction as a decimal.<\/li>\n<li>[latex]\\frac{3}{8}=0.375[\/latex]<\/li>\n<li>Move the decimal two spots to the right.<br \/>\n[latex]\\begin{equation}\\begin{split}&\\curvearrowright \\\\ 0&.375=37.5\\end{split}\\end{equation}[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%;\">\n<caption>Convert [latex]\\frac{3}{8}[\/latex] to a percentage<\/caption>\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 25%;\">[latex]\\frac{3}{8} = \\text{_____}\\%[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Use long division to write fraction as a decimal.<\/td>\n<td style=\"width: 25%;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1264\" src=\"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.47.44-PM.png\" alt=\"A long division equation showing that 3 divided by 8 equals 0.375.\" width=\"86\" height=\"146\" srcset=\"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.47.44-PM.png 430w, https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.47.44-PM-177x300.png 177w, https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.47.44-PM-65x110.png 65w, https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.47.44-PM-225x382.png 225w, https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.47.44-PM-350x594.png 350w\" sizes=\"auto, (max-width: 86px) 100vw, 86px\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 25%;\">[latex]\\frac{3}{8} = 0.375[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Move the decimal point two places to the right and add the percent sign.<\/td>\n<td style=\"width: 25%;\">[latex]0.375 = 37.5\\%[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%; height: 142px;\">\n<caption>Convert [latex]\\frac{1}{3}[\/latex] to a percentage<\/caption>\n<tbody>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\"><\/td>\n<td style=\"width: 25%; height: 16px;\">[latex]\\frac{1}{3} = \\text{_____}\\%[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 77px;\">\n<td style=\"width: 50%; height: 77px;\">Use long division to write fraction as a decimal.<\/td>\n<td style=\"width: 25%; height: 77px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1265\" src=\"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.47.51-PM.png\" alt=\"A long division equation showing that 1 divided by 3 equals 0.333 repeating.\" width=\"97\" height=\"78\" srcset=\"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.47.51-PM.png 354w, https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.47.51-PM-300x241.png 300w, https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.47.51-PM-65x52.png 65w, https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.47.51-PM-225x181.png 225w, https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.47.51-PM-350x281.png 350w\" sizes=\"auto, (max-width: 97px) 100vw, 97px\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\"><\/td>\n<td style=\"width: 25%; height: 16px;\">[latex]\\frac{1}{3} = 0.33\\overline{3}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 33px;\">\n<td style=\"width: 50%; height: 33px;\">Move the decimal point two places to the right and add the percent sign.<\/td>\n<td style=\"width: 25%; height: 33px;\">[latex]0.33\\overline{3}=33.\\overline{3}\\% \\text{ also written as } 33\\frac{1}{3}\\%[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%; height: 64px;\">\n<caption>Convert [latex]\\frac{11}{12}[\/latex] to a percentage<\/caption>\n<tbody>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\"><\/td>\n<td style=\"width: 25%; height: 16px;\">[latex]\\frac{11}{12} = \\text{_____}\\%[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">Use long division to write fraction as a decimal.<\/td>\n<td style=\"width: 25%; height: 16px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1266\" src=\"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.47.58-PM.png\" alt=\"A long division equation showing that 11 divided by 12 equals 0.9166 repeating.\" width=\"93\" height=\"177\" srcset=\"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.47.58-PM.png 454w, https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.47.58-PM-158x300.png 158w, https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.47.58-PM-65x123.png 65w, https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.47.58-PM-225x426.png 225w, https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.47.58-PM-350x663.png 350w\" sizes=\"auto, (max-width: 93px) 100vw, 93px\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\"><\/td>\n<td style=\"width: 25%; height: 16px;\">[latex]\\frac{11}{12} = 0.91\\overline{6}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">\u00a0Move the decimal point two places to the right and add the percent sign.<\/td>\n<td style=\"width: 25%; height: 16px;\">[latex]0.916\\overline{6} = 91.\\overline{6}\\%[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol type=\"A\">\n<li>[latex]\\tfrac{1}{12}=0.08\\overline{3} \\ \\ \\ \\ \\ \\ 0.08\\overline{3}\\times100\\%=8.\\overline{3}\\%[\/latex]<\/li>\n<li>[latex]\\tfrac{1}{8}[\/latex]<\/li>\n<li>[latex]\\tfrac{5}{8}[\/latex]<\/li>\n<li>[latex]\\tfrac{7}{8}[\/latex]<\/li>\n<li>[latex]\\tfrac{2}{3}[\/latex]<\/li>\n<li>[latex]\\tfrac{5}{16}[\/latex]<\/li>\n<li>[latex]\\tfrac{5}{6}[\/latex]<\/li>\n<li>[latex]\\tfrac{4}{9}[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 7<\/strong><\/p>\n<ol start=\"2\" type=\"A\">\n<li>[latex]12.5\\%[\/latex]<\/li>\n<li>[latex]62.5\\%[\/latex]<\/li>\n<li>[latex]87.5\\%[\/latex]<\/li>\n<li>[latex]66.\\overline{6}\\%[\/latex]<\/li>\n<li>[latex]31.25\\%[\/latex]<\/li>\n<li>[latex]83.\\overline{3}\\%[\/latex]<\/li>\n<li>[latex]44.\\overline{4}\\%[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p>The method you use to change a common fraction to a percent will depend on the numbers you are working with. Choose whichever method seems easier for the situation. You will also memorize many equivalencies as you work with them. But you should definitely memorize:<\/p>\n<ul>\n<li>[latex]\\tfrac{1}{3}=33\\tfrac{1}{3}\\%[\/latex]<\/li>\n<li>[latex]\\tfrac{2}{3}=66\\tfrac{2}{3}\\%[\/latex]<\/li>\n<\/ul>\n<h1>Changing Percents to Common Fractions<\/h1>\n<p>You know that percents are a form of fraction with an unwritten denominator of 100. A % sign is used.<\/p>\n<div class=\"textbox shaded\">To change any percent to a decimal, common fraction, or mixed number, divide by 100 and remove the percent sign.<\/div>\n<p><strong>To change a percent to a common fraction:<\/strong><\/p>\n<ul>\n<li>Write the numerals in the percent as the numerator.<\/li>\n<li>Write 100 as the denominator. (Remember that the line in a fraction can be a divided by sign, so [latex]58\\%=\\tfrac{58}{100}[\/latex] is the same as [latex]58\\div100[\/latex].)<\/li>\n<li>Remove the % sign.<\/li>\n<li>Simplify the fraction: [latex]\\tfrac{58}{100}=\\tfrac{29}{50}[\/latex]<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example A<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Write each percent as a common fraction.<\/p>\n<p>[latex]38\\%=\\dfrac{38}{100}\\div\\left(\\dfrac{2}{2}\\right)= \\dfrac{38 \\div 2}{100 \\div 2} =\\dfrac{19}{50}[\/latex]<\/p>\n<p>[latex]25\\%=\\dfrac{25}{100}\\div\\left(\\dfrac{25}{25}\\right)= \\dfrac{25    \\div 25 }{100 \\div 25}=\\dfrac{1}{4}[\/latex]<\/p>\n<p>[latex]3\\%=\\dfrac{3}{100}[\/latex]<\/p>\n<\/div>\n<\/div>\n<p>Note that <strong>percents greater than or equal to 100 become improper fractions<\/strong> which will be rewritten as mixed numbers.<\/p>\n<p>[latex]110\\%=\\tfrac{110}{100}=1\\tfrac{10}{100}=1\\tfrac{1}{10}[\/latex] <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1268\" src=\"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.52.46-PM.png\" alt=\"A long division equation showing that 110 divided by 100 is 1 with 10 remaining.\" width=\"73\" height=\"92\" srcset=\"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.52.46-PM.png 490w, https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.52.46-PM-239x300.png 239w, https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.52.46-PM-65x82.png 65w, https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.52.46-PM-225x283.png 225w, https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.52.46-PM-350x440.png 350w\" sizes=\"auto, (max-width: 73px) 100vw, 73px\" \/><\/p>\n<p>[latex]120\\%=\\tfrac{120}{100}=1\\tfrac{20}{100}=1\\tfrac{1}{5}[\/latex] <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1269\" src=\"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.52.53-PM.png\" alt=\"A long division equation showing that 120 divided by 100 is 1 with 20 remaining.\" width=\"72\" height=\"101\" srcset=\"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.52.53-PM.png 484w, https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.52.53-PM-214x300.png 214w, https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.52.53-PM-65x91.png 65w, https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.52.53-PM-225x315.png 225w, https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-content\/uploads\/sites\/1470\/2021\/07\/Screenshot-2022-02-15-at-1.52.53-PM-350x490.png 350w\" sizes=\"auto, (max-width: 72px) 100vw, 72px\" \/><\/p>\n<p>Remember 100% is the whole thing. [latex]100\\%=1[\/latex].<\/p>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Change each percent to a common fraction. Simplify to lowest terms.<\/p>\n<ol type=\"A\">\n<li>[latex]31\\%=[\/latex]<\/li>\n<li>[latex]11\\%=[\/latex]<\/li>\n<li>[latex]2\\%=[\/latex]<\/li>\n<li>[latex]20\\%=[\/latex]<\/li>\n<li>[latex]75\\%=[\/latex]<\/li>\n<li>[latex]100\\%=[\/latex]<\/li>\n<li>[latex]750\\%=[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 8<\/strong><\/p>\n<ol type=\"A\">\n<li>[latex]\\tfrac{31}{100}[\/latex]<\/li>\n<li>[latex]\\tfrac{11}{100}[\/latex]<\/li>\n<li>[latex]\\tfrac{1}{50}[\/latex]<\/li>\n<li>[latex]\\tfrac{1}{5}[\/latex]<\/li>\n<li>[latex]\\tfrac{3}{4}[\/latex]<\/li>\n<li>[latex]1[\/latex]<\/li>\n<li>[latex]7\\tfrac{1}{2}[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<h1>Percents Less Than 1%<\/h1>\n<p>Sometimes a percent <strong>smaller than 1%<\/strong> is used. For example, you will hear amounts such as [latex]\\tfrac{1}{4}\\%[\/latex] or [latex]\\tfrac{1}{8}\\%[\/latex] or [latex]\\tfrac{1}{2}\\%[\/latex] on the news about the Bank of Canada rate and the rise and fall of inflation. These are small amounts. Sometimes the expression \u201c[latex]\\tfrac{1}{2}\\text{ of a percentage point}[\/latex]\u201d is used instead of \u201c[latex]\\tfrac{1}{2}\\%[\/latex]\u201d.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>What is [latex]\\tfrac{1}{4}\\%[\/latex]?<\/strong><\/p>\n<p>[latex]\\tfrac{1}{4}\\%[\/latex] is [latex]\\tfrac{1}{4}\\text{ of }1\\%[\/latex]<\/p>\n<p>[latex]1\\%=\\tfrac{1}{100}[\/latex], so [latex]\\tfrac{1}{4}\\text{ of }1\\%=\\tfrac{1}{4}\\times\\tfrac{1}{100}=\\tfrac{1}{400}[\/latex]<\/p>\n<p>[latex]\\tfrac{1}{4}\\%=0.25\\%=0.0025[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p><strong>What is [latex]\\tfrac{1}{2}\\%[\/latex]?<\/strong><\/p>\n<p>[latex]\\tfrac{1}{2}\\%=\\tfrac{1}{2}\\text{ of }1\\%=\\tfrac{1}{2}\\times\\tfrac{1}{100}=\\tfrac{1}{200}[\/latex]<\/p>\n<p>[latex]\\tfrac{1}{2}\\%=0.5\\%=0.005[\/latex]<br \/>\nTo work with percents less than 1%, change the percent to a decimal by dividing by 100 (move decimal point two places to the left).<\/p>\n<p>[latex]0.2\\%=0.002[\/latex]<br \/>\n[latex]0.75\\%=0.0075[\/latex]<\/p>\n<div class=\"textbox shaded\">\n<p><strong>If the percent is expressed as a common fraction, do this:<\/strong><\/p>\n<ul>\n<li>Write the common fraction percent as a decimal percent.<\/li>\n<li>Divide by 100 (move decimal point two places left).<\/li>\n<\/ul>\n<p>[latex]\\begin{equation}\\begin{split}  \\tfrac{1}{2}\\% &= 0.5\\% &= 0.005 \\\\  \\tfrac{1}{4}\\% &= 0.0025\\% &= 0.0025 \\\\  \\tfrac{1}{8}\\% &= 0.00125\\% &= 0.00125  \\end{split}\\end{equation}[\/latex]<\/p>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Change each percent to an equivalent decimal.<\/p>\n<ol type=\"A\">\n<li>[latex]\\tfrac{1}{2}\\%=[\/latex]<\/li>\n<li>[latex]0.6\\%=[\/latex]<\/li>\n<li>[latex]\\tfrac{3}{10}\\%=[\/latex]<\/li>\n<li>[latex]\\tfrac{3}{5}\\%=[\/latex]<\/li>\n<li>[latex]0.75\\%=[\/latex]<\/li>\n<li>[latex]\\tfrac{3}{4}\\%=[\/latex]<\/li>\n<li>[latex]0.5\\%=[\/latex]<\/li>\n<li>[latex]\\tfrac{1}{4}\\%=[\/latex]<\/li>\n<li>[latex]0.125\\%=[\/latex]<\/li>\n<li>[latex]\\tfrac{5}{8}\\%=[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 9<\/strong><\/p>\n<ol type=\"A\">\n<li>[latex]0.005[\/latex]<\/li>\n<li>[latex]0.006[\/latex]<\/li>\n<li>[latex]0.003[\/latex]<\/li>\n<li>[latex]0.006[\/latex]<\/li>\n<li>[latex]0.0075[\/latex]<\/li>\n<li>[latex]0.0075[\/latex]<\/li>\n<li>[latex]0.005[\/latex]<\/li>\n<li>[latex]0.0025[\/latex]<\/li>\n<li>[latex]0.00125[\/latex]<\/li>\n<li>[latex]0.00625[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<h1>16\u2154%, 33\u2153%, 66\u2154%, 83\u2153% &#8230;<\/h1>\n<p>These percents will become repeating decimals. For example:<\/p>\n<p>[latex]\\begin{equation}\\begin{split}  33\\tfrac{1}{3}\\% &= 33.\\overline{3}\\% &= 0.33\\overline{3} \\\\  \\\\  66\\tfrac{2}{3}\\% &= 66.\\overline{6}\\% &= 0.66\\overline{6}  \\end{split}\\end{equation}[\/latex]<\/p>\n<p>It is usually more convenient to use the common fraction equivalent of these percents. Memorize them, or make a note on a special paper and post it near your work space.<\/p>\n<p>[latex]\\begin{equation}\\begin{split}  33\\tfrac{1}{3}\\% &= 33\\tfrac{1}{3}\\div100 &= \\tfrac{100}{3}\\times\\tfrac{1}{100} \\ &= \\tfrac{1}{3} \\\\  \\\\  66\\tfrac{2}{3}\\% &= 66\\tfrac{2}{3}\\div100 &= \\tfrac{200}{3}\\times\\tfrac{1}{100} \\ &= \\tfrac{2}{3}  \\end{split}\\end{equation}[\/latex]<\/p>\n<div class=\"textbox shaded\">[latex]\\begin{equation}\\begin{split}  16\\tfrac{2}{3}\\% &= \\tfrac{1}{6} \\\\  \\\\  33\\tfrac{1}{3}\\% &= \\tfrac{1}{3} \\\\  \\\\  66\\tfrac{2}{3}\\% &= \\tfrac{2}{3} \\\\  \\\\  83\\tfrac{1}{3}\\% &= \\tfrac{5}{6}  \\end{split}\\end{equation}[\/latex]<\/div>\n<p>&nbsp;<\/p>\n<h1>Review of Equivalent Common Fractions, Decimals, and Percents<\/h1>\n<p>Complete this chart. These are equivalents that you will often use, so use this chart for reference. Memorize as many equivalents as you can. You may wish to put other equivalents on the chart.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<th style=\"width: 33.3%; text-align: center;\" scope=\"col\">Common Fraction<\/th>\n<th style=\"width: 33.3%; text-align: center; vertical-align: top;\" scope=\"col\">Decimal<\/th>\n<th style=\"width: 33.3%; text-align: center; vertical-align: top;\" scope=\"col\">Percent<\/th>\n<\/tr>\n<tr>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]\\tfrac{1}{4}[\/latex]<\/td>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\"><\/td>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\"><\/td>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]0.5[\/latex]<\/td>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\"><\/td>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\"><\/td>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]75\\%[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]\\tfrac{1}{8}[\/latex]<\/td>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\"><\/td>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\"><\/td>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]0.375[\/latex]<\/td>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\"><\/td>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\"><\/td>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]62.5\\%[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"textbox shaded\">\n<p><strong>Answers to Review of Equivalent Common Fractions, Decimals, and Percents<\/strong><\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<th style=\"width: 33.3%; text-align: center;\" scope=\"col\">Common Fraction<\/th>\n<th style=\"width: 33.3%; text-align: center; vertical-align: top;\" scope=\"col\">Decimal<\/th>\n<th style=\"width: 33.3%; text-align: center; vertical-align: top;\" scope=\"col\">Percent<\/th>\n<\/tr>\n<tr>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]\\tfrac{1}{4}[\/latex]<\/td>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]0.25[\/latex]<\/td>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]25\\%[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]\\tfrac{1}{2}[\/latex]<\/td>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]0.5[\/latex]<\/td>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]50\\%[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]\\tfrac{3}{4}[\/latex]<\/td>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]0.75[\/latex]<\/td>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]75\\%[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]\\tfrac{1}{8}[\/latex]<\/td>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]0.125[\/latex]<\/td>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]12.5\\%[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]\\tfrac{3}{8}[\/latex]<\/td>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]0.375[\/latex]<\/td>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]37.5\\%[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]\\tfrac{5}{8}[\/latex]<\/td>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]0.625[\/latex]<\/td>\n<td style=\"width: 33.3%; text-align: center;\" scope=\"col\">[latex]62.5\\%[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<h1>Topic A: Self-Test<\/h1>\n<p><strong>Mark\u00a0 \u00a0 \u00a0 \u00a0\/15\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Aim\u00a0 \u00a0 \u00a0 \u00a0 13\/15<\/strong><\/p>\n<ol type=\"A\">\n<li>Write these percents in numeral form.<br \/>\n<strong>(2 marks)<\/strong><\/p>\n<ol type=\"i\">\n<li>Sixty-two and one-half percent<\/li>\n<li>One hundred six and one-fifth percent<\/li>\n<\/ol>\n<p>&nbsp;<\/li>\n<li>Write these percents in words.<br \/>\n<strong>(2 marks)<\/strong><\/p>\n<ol type=\"i\">\n<li>[latex]72\\%[\/latex]<\/li>\n<li>[latex]\\tfrac{3}{4}\\%[\/latex]<\/li>\n<\/ol>\n<p>&nbsp;<\/li>\n<li>Change the percents to decimal fractions.<br \/>\n<strong>(5 marks)<\/strong><\/p>\n<ol type=\"i\">\n<li>[latex]32\\%[\/latex]<\/li>\n<li>[latex]18.5\\%[\/latex]<\/li>\n<li>[latex]125\\%[\/latex]<\/li>\n<li>[latex]\\tfrac{4}{5}\\%[\/latex]<\/li>\n<li>[latex]\\tfrac{2}{3}\\%[\/latex]<\/li>\n<\/ol>\n<p>&nbsp;<\/li>\n<li>Change these percents to common fractions in lowest terms.<br \/>\n<strong>(4 marks)<\/strong><\/p>\n<ol type=\"i\">\n<li>[latex]16\\%[\/latex]<\/li>\n<li>[latex]20\\%[\/latex]<\/li>\n<li>[latex]106\\%[\/latex]<\/li>\n<li>[latex]75\\%[\/latex]<\/li>\n<\/ol>\n<p>&nbsp;<\/li>\n<li>Change these common fractions to equivalent percents.<br \/>\n<strong>(2 marks)<\/strong><\/p>\n<ol type=\"i\">\n<li>[latex]\\tfrac{4}{5}[\/latex]<\/li>\n<li>[latex]\\tfrac{3}{8}[\/latex]<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p>&nbsp;<\/p>\n<div class=\"textbox shaded\">\n<p><strong>Answers to Topic A Self-Test<\/strong><\/p>\n<ol type=\"A\">\n<li style=\"list-style-type: none;\">\n<ol type=\"i\">\n<li>[latex]62.5\\%[\/latex] or [latex]62\\tfrac{1}{2}\\%[\/latex]<\/li>\n<li>[latex]106.2\\%[\/latex] or [latex]106\\tfrac{1}{5}\\%[\/latex]<\/li>\n<\/ol>\n<ol type=\"i\">\n<li>Seventy-two percent<\/li>\n<li>Three-quarters percent<\/li>\n<\/ol>\n<ol type=\"i\">\n<li>[latex]0.32[\/latex]<\/li>\n<li>[latex]0.185[\/latex]<\/li>\n<li>[latex]1.25[\/latex]<\/li>\n<li>[latex]0.008[\/latex]<\/li>\n<li>[latex]0.00\\overline{6}[\/latex]<\/li>\n<\/ol>\n<ol type=\"i\">\n<li>[latex]\\tfrac{4}{25}[\/latex]<\/li>\n<li>[latex]\\tfrac{1}{5}[\/latex]<\/li>\n<li>[latex]1\\tfrac{3}{50}[\/latex]<\/li>\n<li>[latex]\\tfrac{3}{4}[\/latex]<\/li>\n<\/ol>\n<ol type=\"i\">\n<li>[latex]80\\%[\/latex]<\/li>\n<li>[latex]37.5\\%[\/latex]<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<\/div>\n","protected":false},"author":103,"menu_order":1,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-34","chapter","type-chapter","status-publish","hentry"],"part":30,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-json\/pressbooks\/v2\/chapters\/34","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-json\/wp\/v2\/users\/103"}],"version-history":[{"count":27,"href":"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-json\/pressbooks\/v2\/chapters\/34\/revisions"}],"predecessor-version":[{"id":1290,"href":"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-json\/pressbooks\/v2\/chapters\/34\/revisions\/1290"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-json\/pressbooks\/v2\/parts\/30"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-json\/pressbooks\/v2\/chapters\/34\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-json\/wp\/v2\/media?parent=34"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-json\/pressbooks\/v2\/chapter-type?post=34"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-json\/wp\/v2\/contributor?post=34"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/alfm6\/wp-json\/wp\/v2\/license?post=34"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}