{"id":3477,"date":"2022-03-02T15:43:51","date_gmt":"2022-03-02T15:43:51","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=3477"},"modified":"2022-04-06T13:56:55","modified_gmt":"2022-04-06T13:56:55","slug":"corequisite-support-activity-for-1e","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/corequisite-support-activity-for-1e\/","title":{"raw":"Corequisite Support Activity for 1E: Collaboration","rendered":"Corequisite Support Activity for 1E: Collaboration"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>What you'll need to know:<\/h3>\r\nIn this support activity you\u2019ll become familiar with the following:\r\n<ul>\r\n \t<li>Compare proportions to answer a statistical question.<\/li>\r\n<\/ul>\r\nYou will also have an opportunity to refresh the following skills:\r\n<ul>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Write a proportion as a simplified fraction.&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:769,&quot;3&quot;:{&quot;1&quot;:0},&quot;11&quot;:4,&quot;12&quot;:0}\">Write a proportion as a simplified fraction.<\/span><\/li>\r\n \t<li>Write a proportion as a decimal.<\/li>\r\n \t<li>Write a proportion as a percentage.<\/li>\r\n<\/ul>\r\n<\/div>\r\nThroughout this class, you will need compute fractions, proportions, and percentages and convert from one numeric representation to another.\r\n<h3>Fractions, Decimals, and Percentages<\/h3>\r\nPart-to-whole relationships, or proportions, can be represented by fractions, decimals, or percentages. It is often helpful to convert between these three forms to assist with data analysis. To change a fraction to a decimal, divide the numerator by the denominator. To change a decimal to a percentage, move the decimal point two places to the right. See the recall box below for a refresher of these skills.\r\n<div class=\"textbox examples\">\r\n<h3>recall<\/h3>\r\nCore skill:\r\n[reveal-answer q=\"165243\"]Simplify a fraction[\/reveal-answer]\r\n[hidden-answer a=\"165243\"]\r\n\r\nOne way to simplify a fraction is to repeatedly divide the top (the numerator) and bottom (the denominator) by common factors until no more common factors exist.\r\n\r\nEx. Simplify the fraction [latex]\\dfrac{9}{12}[\/latex]\r\n<p style=\"padding-left: 30px;\">We know that [latex]3[\/latex] divides evenly (without a remainder) into both 9 and 12, so let's divide by 3 in the top and the bottom.<\/p>\r\n<p style=\"padding-left: 30px;\">[latex]\\dfrac{9}{12}=\\dfrac{3}{4}[\/latex]<\/p>\r\n<p style=\"padding-left: 30px;\">Since there are no factors common to both [latex]3[\/latex] and [latex]4[\/latex], we are done.<\/p>\r\n[\/hidden-answer]\r\n\r\nCore skill:\u00a0[reveal-answer q=\"55482\"]Convert a fraction to a decimal[\/reveal-answer]\r\n[hidden-answer a=\"55482\"]To convert a fraction to a decimal, use a calculator to divide the numerator by the denominator.\r\n\r\nEx. Convert the fraction [latex]\\dfrac{9}{12}[\/latex] to a decimal.\r\n<p style=\"padding-left: 30px;\">To do so, divide the numerator by the denominator. You can use your calculator.<\/p>\r\n<p style=\"padding-left: 30px;\">[latex]9\\div12=0.75[\/latex]<\/p>\r\n<p style=\"padding-left: 30px;\">[\/hidden-answer]<\/p>\r\nCore skill:\u00a0[reveal-answer q=\"238058\"]Rounding decimals[\/reveal-answer]\r\n[hidden-answer a=\"238058\"]When converting fractions to decimals, sometimes we end up with a \"long\" decimal (one with many digits after the decimal point). You can shorten the decimal by rounding to a desired number of decimal places.\r\n\r\nEx. Convert the fraction [latex]\\dfrac{4}{17}[\/latex] to a decimal and round to the nearest hundredth (two decimal places).\r\n<p style=\"padding-left: 30px;\">[latex]4\\div17=0.2352941176[\/latex]<\/p>\r\n<p style=\"padding-left: 30px;\">To round to 2 decimal places, we need to make a decision to round up or round down. Look to the number to the right of the place we want to round to. We see there is a [latex]5[\/latex] to the right of the hundredths place. If the number to the right is [latex]5[\/latex] or higher, we'll round up.<\/p>\r\n<p style=\"padding-left: 30px;\">The rounded result will be [latex]0.24[\/latex].<\/p>\r\nEx. Convert the fraction\u00a0[latex]\\dfrac{4}{17}[\/latex] to a decimal and round to the nearest tenth (one decimal place).\r\n<p style=\"padding-left: 30px;\">[latex]4\\div17=0.2352941176[\/latex]<\/p>\r\n<p style=\"padding-left: 30px;\">To round to 1 decimal place, we we see there is a [latex]3[\/latex] to the right of the hundredths place. If the number to the right is [latex]4[\/latex] or smaller, we'll round down.<\/p>\r\n<p style=\"padding-left: 30px;\">The rounded result will be [latex]0.2[\/latex].<\/p>\r\n[\/hidden-answer]\r\n\r\nCore skill:\u00a0[reveal-answer q=\"613555\"]Convert a decimal to a percentage[\/reveal-answer]\r\n[hidden-answer a=\"613555\"]To convert a decimal to a percentage, move the decimal point two places to the right (multiply by 100) and append the percent symbol [latex]\\%[\/latex].\r\n\r\nEx. Convert the fraction\u00a0[latex]\\dfrac{4}{17}[\/latex] to a percentage, rounded to the nearest hundredth.\r\n<p style=\"padding-left: 30px;\">[latex]\\dfrac{4}{17}=0.23529...[\/latex]<\/p>\r\n<p style=\"padding-left: 30px;\">Move the decimal two places to the right to obtain [latex]23.529...[\/latex].<\/p>\r\n<p style=\"padding-left: 30px;\">Round to the hundredths place and append the percent symbol.<\/p>\r\n<p style=\"padding-left: 30px;\">[latex]23.53\\%[\/latex]<\/p>\r\n[\/hidden-answer]\r\n\r\n<span style=\"background-color: #ffff99;\">[link to student resource: Fractions, Decimals, Percentages]<\/span>\r\n\r\n<span style=\"background-color: #ffff99;\">[link to student resource: Rounding and Estimation]<\/span>\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\n<strong>Example:<\/strong> Twenty-four students are enrolled in one section of a statistics course. On Friday, 18 students were present in class. What proportion of the students were present on Friday? Give your answer as a simplified fraction, a decimal rounded to the nearest hundredth, and a percentage.\r\n\r\n<strong>Solution:<\/strong>\r\n<div align=\"left\">\r\n<table style=\"width: 441px; height: 234px;\">\r\n<tbody>\r\n<tr style=\"height: 99px;\">\r\n<td style=\"width: 149.172px; height: 99px;\">Reduced Fraction<\/td>\r\n<td style=\"width: 137.156px; height: 99px;\">Decimal<\/td>\r\n<td style=\"width: 116.172px; height: 99px;\">Percentage<\/td>\r\n<\/tr>\r\n<tr style=\"height: 135px;\">\r\n<td style=\"width: 149.172px; height: 135px;\">[latex]\\frac{18}{24}= \\frac{3}{4}[\/latex]<\/td>\r\n<td style=\"width: 137.156px; height: 135px;\">[latex]\\frac{3}{4}= \\frac{75}{100}= 0.75[\/latex]<\/td>\r\n<td style=\"width: 116.172px; height: 135px;\">0.75 = 75%<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWhen you use a calculator to convert a fraction to a decimal, you may get a \u201cshort\u201d decimal representation like this:\r\n\r\n[latex]\\frac{15}{25}=0.6[\/latex]\r\n\r\nOther times, you may get a \u201clong\u201d decimal representation like this:\r\n\r\n[latex]\\frac{1}{28}=0.03571428571[\/latex]\r\n\r\nWhen you get a \u201clong\u201d representation, you can shorten the decimal by <strong>rounding.<\/strong>\r\n\r\nRound\u00a0[latex]0.03571428571[\/latex] to the nearest thousandth then convert to a percentage.\r\n\r\n[reveal-answer q=\"818149\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"818149\"][latex]0.0357 = 3.57\\%[\/latex][\/hidden-answer]\r\n\r\nRound\u00a0[latex]0.03571428571[\/latex] to the nearest hundredth then convert to a percentage.\r\n\r\n[reveal-answer q=\"221698\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"221698\"][latex]0.036 = 3.6\\%[\/latex][\/hidden-answer][\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\nNow you try rounding by answering Question 1.\r\n<div align=\"left\">\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 1<\/h3>\r\nConvert [latex]\\frac{5}{8}[\/latex] to a decimal, and then round your answer as follows:\r\n\r\nPart A: Round to the nearest tenth.\r\n\r\n[reveal-answer q=\"481262\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"481262\"]See the Recall box above to refresh this skill if needed.[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\nPart B: Round to the nearest hundredth.\r\n\r\n[reveal-answer q=\"411797\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"411797\"]See the Recall box above to refresh this skill if needed.[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\nPart C: Round to the nearest thousandth.\r\n\r\n[reveal-answer q=\"889699\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"889699\"]See the Recall box above to refresh this skill if needed.[\/hidden-answer]\r\n\r\n<\/div>\r\nLet's put all of these skills together to make some comparisons about proportions of students enrolled in a large statistics class. Remember a proportion is a part-to-whole relationship. See the summary in the example below to assess your understanding before completing Question 2.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nA proportion is a part-to-whole relationship that can be expressed as a fraction, a decimal, or a percentage.\r\n\r\nEx. If eight students in a class of 32 students were absent one day, what proportion of students were absent? Give your answer in the form of a simplified fraction, decimal, and percentage.\r\n\r\n[reveal-answer q=\"412288\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"412288\"]\r\n\r\n[latex]\\dfrac{8}{32}=\\dfrac{1}{4}=0.25=25%[\/latex][\/hidden-answer]\r\n\r\n<\/div>\r\nNow it's your turn. In Question 2, first fill in the table from information in the given paragraph. Make sure to check the accuracy of your completed table before continuing on! All the rest of the questions depend on it.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 2<\/h3>\r\nAt a certain college, 150 students are enrolled in a statistics class. Of the 150 students, 45 live on campus and 105 live off campus. The professor was curious about whether her students study in the campus library. Of those who live on campus, 20 said they prefer to study in the library. Of those who live off campus, 40 said they prefer to study in the library.\r\n\r\n&nbsp;\r\n\r\nPart A: Organize the data by completing the following table.\r\n\r\n&nbsp;\r\n<div align=\"left\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>Prefer to study\r\nat the library<\/td>\r\n<td>Prefer to study\r\nelsewhere<\/td>\r\n<td>Total<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Live on campus<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Live off campus<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Total<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[reveal-answer q=\"546386\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"546386\"]Did you check the accuracy of your completed table?[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nPart B: What proportion of the students enrolled in this statistics class live on campus? Give your answer as a simplified fraction, a decimal, and a percentage rounded to the nearest whole percentage point.\r\n\r\n[reveal-answer q=\"728274\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"728274\"]A proportion is a part-to-whole relationship: [latex]\\frac{\\text{part}}{\\text{whole}}[\/latex].Make sure your table entries are accurate. See the Recall box and Examples above for how to simplify fractions and convert.[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\nPart C: What proportion of the students enrolled in this statistics class live off campus? Give your answer as a simplified fraction, a decimal, and a percentage rounded to the nearest whole percentage point.\r\n\r\n[reveal-answer q=\"861738\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"861738\"]A proportion is a part-to-whole relationship: [latex]\\frac{\\text{part}}{\\text{whole}}[\/latex].Make sure your table entries are accurate. See the Recall box and Examples above for how to simplify fractions and convert.[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\nPart D: What proportion of the students enrolled in this statistics class prefer to study at the library? Give your answer as a simplified fraction, a decimal, and a percentage rounded to the nearest whole percentage point.\r\n\r\n[reveal-answer q=\"986831\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"986831\"]A proportion is a part-to-whole relationship: [latex]\\frac{\\text{part}}{\\text{whole}}[\/latex].Make sure your table entries are accurate. See the Recall box and Examples above for how to simplify fractions and convert.[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\nPart E: What proportion of the students who live on campus prefer to study at the library? Give your answer as a simplified fraction, a decimal rounded to the nearest hundredth, and a percentage rounded to the nearest whole percentage point.\r\n\r\n[reveal-answer q=\"271998\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"271998\"]A proportion is a part-to-whole relationship: [latex]\\frac{\\text{part}}{\\text{whole}}[\/latex].Make sure your table entries are accurate. See the Recall box and Examples above for how to simplify fractions and convert.[\/hidden-answer]\r\n\r\nPart F: What proportion of the students who live off campus prefer to study at the library? Give your answer as a simplified fraction, a decimal rounded to the nearest hundredth, and a percentage rounded to the nearest whole percentage point.\r\n\r\n&nbsp;\r\n\r\nPart G: In which group (those who live on campus or those who live off campus) were students more likely to prefer studying at the library?\r\n\r\n[reveal-answer q=\"270529\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"270529\"]What do <em>you<\/em> think?[\/hidden-answer]\r\n\r\n<\/div>\r\nIf you find that you aren't quite comfortable yet with converting fractions to decimals and percentages, visit the Student Resource Fractions, Decimals, Percentages for more support. Your instructor may also have resources to help. You'll continue to practice these skills throughout the course though, and they will become less challenging the more you use them. Let's move on to the\u00a0<em>What to Know<\/em> to learn about the powerful benefit of forming study groups in college.\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>What you&#8217;ll need to know:<\/h3>\n<p>In this support activity you\u2019ll become familiar with the following:<\/p>\n<ul>\n<li>Compare proportions to answer a statistical question.<\/li>\n<\/ul>\n<p>You will also have an opportunity to refresh the following skills:<\/p>\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Write a proportion as a simplified fraction.&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:769,&quot;3&quot;:{&quot;1&quot;:0},&quot;11&quot;:4,&quot;12&quot;:0}\">Write a proportion as a simplified fraction.<\/span><\/li>\n<li>Write a proportion as a decimal.<\/li>\n<li>Write a proportion as a percentage.<\/li>\n<\/ul>\n<\/div>\n<p>Throughout this class, you will need compute fractions, proportions, and percentages and convert from one numeric representation to another.<\/p>\n<h3>Fractions, Decimals, and Percentages<\/h3>\n<p>Part-to-whole relationships, or proportions, can be represented by fractions, decimals, or percentages. It is often helpful to convert between these three forms to assist with data analysis. To change a fraction to a decimal, divide the numerator by the denominator. To change a decimal to a percentage, move the decimal point two places to the right. See the recall box below for a refresher of these skills.<\/p>\n<div class=\"textbox examples\">\n<h3>recall<\/h3>\n<p>Core skill:<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q165243\">Simplify a fraction<\/span><\/p>\n<div id=\"q165243\" class=\"hidden-answer\" style=\"display: none\">\n<p>One way to simplify a fraction is to repeatedly divide the top (the numerator) and bottom (the denominator) by common factors until no more common factors exist.<\/p>\n<p>Ex. Simplify the fraction [latex]\\dfrac{9}{12}[\/latex]<\/p>\n<p style=\"padding-left: 30px;\">We know that [latex]3[\/latex] divides evenly (without a remainder) into both 9 and 12, so let&#8217;s divide by 3 in the top and the bottom.<\/p>\n<p style=\"padding-left: 30px;\">[latex]\\dfrac{9}{12}=\\dfrac{3}{4}[\/latex]<\/p>\n<p style=\"padding-left: 30px;\">Since there are no factors common to both [latex]3[\/latex] and [latex]4[\/latex], we are done.<\/p>\n<\/div>\n<\/div>\n<p>Core skill:\u00a0<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q55482\">Convert a fraction to a decimal<\/span><\/p>\n<div id=\"q55482\" class=\"hidden-answer\" style=\"display: none\">To convert a fraction to a decimal, use a calculator to divide the numerator by the denominator.<\/p>\n<p>Ex. Convert the fraction [latex]\\dfrac{9}{12}[\/latex] to a decimal.<\/p>\n<p style=\"padding-left: 30px;\">To do so, divide the numerator by the denominator. You can use your calculator.<\/p>\n<p style=\"padding-left: 30px;\">[latex]9\\div12=0.75[\/latex]<\/p>\n<p style=\"padding-left: 30px;\"><\/div>\n<\/div>\n<p>Core skill:\u00a0<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q238058\">Rounding decimals<\/span><\/p>\n<div id=\"q238058\" class=\"hidden-answer\" style=\"display: none\">When converting fractions to decimals, sometimes we end up with a &#8220;long&#8221; decimal (one with many digits after the decimal point). You can shorten the decimal by rounding to a desired number of decimal places.<\/p>\n<p>Ex. Convert the fraction [latex]\\dfrac{4}{17}[\/latex] to a decimal and round to the nearest hundredth (two decimal places).<\/p>\n<p style=\"padding-left: 30px;\">[latex]4\\div17=0.2352941176[\/latex]<\/p>\n<p style=\"padding-left: 30px;\">To round to 2 decimal places, we need to make a decision to round up or round down. Look to the number to the right of the place we want to round to. We see there is a [latex]5[\/latex] to the right of the hundredths place. If the number to the right is [latex]5[\/latex] or higher, we&#8217;ll round up.<\/p>\n<p style=\"padding-left: 30px;\">The rounded result will be [latex]0.24[\/latex].<\/p>\n<p>Ex. Convert the fraction\u00a0[latex]\\dfrac{4}{17}[\/latex] to a decimal and round to the nearest tenth (one decimal place).<\/p>\n<p style=\"padding-left: 30px;\">[latex]4\\div17=0.2352941176[\/latex]<\/p>\n<p style=\"padding-left: 30px;\">To round to 1 decimal place, we we see there is a [latex]3[\/latex] to the right of the hundredths place. If the number to the right is [latex]4[\/latex] or smaller, we&#8217;ll round down.<\/p>\n<p style=\"padding-left: 30px;\">The rounded result will be [latex]0.2[\/latex].<\/p>\n<\/div>\n<\/div>\n<p>Core skill:\u00a0<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q613555\">Convert a decimal to a percentage<\/span><\/p>\n<div id=\"q613555\" class=\"hidden-answer\" style=\"display: none\">To convert a decimal to a percentage, move the decimal point two places to the right (multiply by 100) and append the percent symbol [latex]\\%[\/latex].<\/p>\n<p>Ex. Convert the fraction\u00a0[latex]\\dfrac{4}{17}[\/latex] to a percentage, rounded to the nearest hundredth.<\/p>\n<p style=\"padding-left: 30px;\">[latex]\\dfrac{4}{17}=0.23529...[\/latex]<\/p>\n<p style=\"padding-left: 30px;\">Move the decimal two places to the right to obtain [latex]23.529...[\/latex].<\/p>\n<p style=\"padding-left: 30px;\">Round to the hundredths place and append the percent symbol.<\/p>\n<p style=\"padding-left: 30px;\">[latex]23.53\\%[\/latex]<\/p>\n<\/div>\n<\/div>\n<p><span style=\"background-color: #ffff99;\">[link to student resource: Fractions, Decimals, Percentages]<\/span><\/p>\n<p><span style=\"background-color: #ffff99;\">[link to student resource: Rounding and Estimation]<\/span><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p><strong>Example:<\/strong> Twenty-four students are enrolled in one section of a statistics course. On Friday, 18 students were present in class. What proportion of the students were present on Friday? Give your answer as a simplified fraction, a decimal rounded to the nearest hundredth, and a percentage.<\/p>\n<p><strong>Solution:<\/strong><\/p>\n<div style=\"text-align: left;\">\n<table style=\"width: 441px; height: 234px;\">\n<tbody>\n<tr style=\"height: 99px;\">\n<td style=\"width: 149.172px; height: 99px;\">Reduced Fraction<\/td>\n<td style=\"width: 137.156px; height: 99px;\">Decimal<\/td>\n<td style=\"width: 116.172px; height: 99px;\">Percentage<\/td>\n<\/tr>\n<tr style=\"height: 135px;\">\n<td style=\"width: 149.172px; height: 135px;\">[latex]\\frac{18}{24}= \\frac{3}{4}[\/latex]<\/td>\n<td style=\"width: 137.156px; height: 135px;\">[latex]\\frac{3}{4}= \\frac{75}{100}= 0.75[\/latex]<\/td>\n<td style=\"width: 116.172px; height: 135px;\">0.75 = 75%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>When you use a calculator to convert a fraction to a decimal, you may get a \u201cshort\u201d decimal representation like this:<\/p>\n<p>[latex]\\frac{15}{25}=0.6[\/latex]<\/p>\n<p>Other times, you may get a \u201clong\u201d decimal representation like this:<\/p>\n<p>[latex]\\frac{1}{28}=0.03571428571[\/latex]<\/p>\n<p>When you get a \u201clong\u201d representation, you can shorten the decimal by <strong>rounding.<\/strong><\/p>\n<p>Round\u00a0[latex]0.03571428571[\/latex] to the nearest thousandth then convert to a percentage.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q818149\">Show Answer<\/span><\/p>\n<div id=\"q818149\" class=\"hidden-answer\" style=\"display: none\">[latex]0.0357 = 3.57\\%[\/latex]<\/div>\n<\/div>\n<p>Round\u00a0[latex]0.03571428571[\/latex] to the nearest hundredth then convert to a percentage.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q221698\">Show Answer<\/span><\/p>\n<div id=\"q221698\" class=\"hidden-answer\" style=\"display: none\">[latex]0.036 = 3.6\\%[\/latex]<\/div>\n<\/div>\n<p>[\/hidden-answer]<\/p>\n<\/div>\n<\/div>\n<p>Now you try rounding by answering Question 1.<\/p>\n<div style=\"text-align: left;\">\n<div class=\"textbox key-takeaways\">\n<h3>question 1<\/h3>\n<p>Convert [latex]\\frac{5}{8}[\/latex] to a decimal, and then round your answer as follows:<\/p>\n<p>Part A: Round to the nearest tenth.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q481262\">Hint<\/span><\/p>\n<div id=\"q481262\" class=\"hidden-answer\" style=\"display: none\">See the Recall box above to refresh this skill if needed.<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Part B: Round to the nearest hundredth.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q411797\">Hint<\/span><\/p>\n<div id=\"q411797\" class=\"hidden-answer\" style=\"display: none\">See the Recall box above to refresh this skill if needed.<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Part C: Round to the nearest thousandth.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q889699\">Hint<\/span><\/p>\n<div id=\"q889699\" class=\"hidden-answer\" style=\"display: none\">See the Recall box above to refresh this skill if needed.<\/div>\n<\/div>\n<\/div>\n<p>Let&#8217;s put all of these skills together to make some comparisons about proportions of students enrolled in a large statistics class. Remember a proportion is a part-to-whole relationship. See the summary in the example below to assess your understanding before completing Question 2.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>A proportion is a part-to-whole relationship that can be expressed as a fraction, a decimal, or a percentage.<\/p>\n<p>Ex. If eight students in a class of 32 students were absent one day, what proportion of students were absent? Give your answer in the form of a simplified fraction, decimal, and percentage.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q412288\">Show Answer<\/span><\/p>\n<div id=\"q412288\" class=\"hidden-answer\" style=\"display: none\">\n<p>[latex]\\dfrac{8}{32}=\\dfrac{1}{4}=0.25=25%[\/latex]<\/p><\/div>\n<\/div>\n<\/div>\n<p>Now it&#8217;s your turn. In Question 2, first fill in the table from information in the given paragraph. Make sure to check the accuracy of your completed table before continuing on! All the rest of the questions depend on it.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 2<\/h3>\n<p>At a certain college, 150 students are enrolled in a statistics class. Of the 150 students, 45 live on campus and 105 live off campus. The professor was curious about whether her students study in the campus library. Of those who live on campus, 20 said they prefer to study in the library. Of those who live off campus, 40 said they prefer to study in the library.<\/p>\n<p>&nbsp;<\/p>\n<p>Part A: Organize the data by completing the following table.<\/p>\n<p>&nbsp;<\/p>\n<div style=\"text-align: left;\">\n<table>\n<tbody>\n<tr>\n<td><\/td>\n<td>Prefer to study<br \/>\nat the library<\/td>\n<td>Prefer to study<br \/>\nelsewhere<\/td>\n<td>Total<\/td>\n<\/tr>\n<tr>\n<td>Live on campus<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Live off campus<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Total<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q546386\">Hint<\/span><\/p>\n<div id=\"q546386\" class=\"hidden-answer\" style=\"display: none\">Did you check the accuracy of your completed table?<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Part B: What proportion of the students enrolled in this statistics class live on campus? Give your answer as a simplified fraction, a decimal, and a percentage rounded to the nearest whole percentage point.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q728274\">Hint<\/span><\/p>\n<div id=\"q728274\" class=\"hidden-answer\" style=\"display: none\">A proportion is a part-to-whole relationship: [latex]\\frac{\\text{part}}{\\text{whole}}[\/latex].Make sure your table entries are accurate. See the Recall box and Examples above for how to simplify fractions and convert.<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Part C: What proportion of the students enrolled in this statistics class live off campus? Give your answer as a simplified fraction, a decimal, and a percentage rounded to the nearest whole percentage point.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q861738\">Hint<\/span><\/p>\n<div id=\"q861738\" class=\"hidden-answer\" style=\"display: none\">A proportion is a part-to-whole relationship: [latex]\\frac{\\text{part}}{\\text{whole}}[\/latex].Make sure your table entries are accurate. See the Recall box and Examples above for how to simplify fractions and convert.<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Part D: What proportion of the students enrolled in this statistics class prefer to study at the library? Give your answer as a simplified fraction, a decimal, and a percentage rounded to the nearest whole percentage point.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q986831\">Hint<\/span><\/p>\n<div id=\"q986831\" class=\"hidden-answer\" style=\"display: none\">A proportion is a part-to-whole relationship: [latex]\\frac{\\text{part}}{\\text{whole}}[\/latex].Make sure your table entries are accurate. See the Recall box and Examples above for how to simplify fractions and convert.<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Part E: What proportion of the students who live on campus prefer to study at the library? Give your answer as a simplified fraction, a decimal rounded to the nearest hundredth, and a percentage rounded to the nearest whole percentage point.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q271998\">Hint<\/span><\/p>\n<div id=\"q271998\" class=\"hidden-answer\" style=\"display: none\">A proportion is a part-to-whole relationship: [latex]\\frac{\\text{part}}{\\text{whole}}[\/latex].Make sure your table entries are accurate. See the Recall box and Examples above for how to simplify fractions and convert.<\/div>\n<\/div>\n<p>Part F: What proportion of the students who live off campus prefer to study at the library? Give your answer as a simplified fraction, a decimal rounded to the nearest hundredth, and a percentage rounded to the nearest whole percentage point.<\/p>\n<p>&nbsp;<\/p>\n<p>Part G: In which group (those who live on campus or those who live off campus) were students more likely to prefer studying at the library?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q270529\">Hint<\/span><\/p>\n<div id=\"q270529\" class=\"hidden-answer\" style=\"display: none\">What do <em>you<\/em> think?<\/div>\n<\/div>\n<\/div>\n<p>If you find that you aren&#8217;t quite comfortable yet with converting fractions to decimals and percentages, visit the Student Resource Fractions, Decimals, Percentages for more support. Your instructor may also have resources to help. You&#8217;ll continue to practice these skills throughout the course though, and they will become less challenging the more you use them. Let&#8217;s move on to the\u00a0<em>What to Know<\/em> to learn about the powerful benefit of forming study groups in college.<\/p>\n<\/div>\n","protected":false},"author":493460,"menu_order":28,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3477","chapter","type-chapter","status-publish","hentry"],"part":3418,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/3477","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/493460"}],"version-history":[{"count":11,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/3477\/revisions"}],"predecessor-version":[{"id":4258,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/3477\/revisions\/4258"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/3418"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/3477\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=3477"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=3477"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=3477"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=3477"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}