{"id":4504,"date":"2013-06-29T06:33:05","date_gmt":"2013-06-29T06:33:05","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=4504"},"modified":"2026-05-01T08:55:39","modified_gmt":"2026-05-01T13:55:39","slug":"ordering-rational-numbers","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/ordering-rational-numbers\/","title":{"rendered":"Ordering Rational Numbers"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_gx7H1O3vrdg\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_gx7H1O3vrdg\" data-source-videoID=\"gx7H1O3vrdg\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Ordering Rational Numbers Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Ordering Rational Numbers\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_gx7H1O3vrdg:hover {cursor:pointer;} img#videoThumbnailImage_gx7H1O3vrdg {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/02\/1277-ordering-rational-numbers-2.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_gx7H1O3vrdg\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_gx7H1O3vrdg\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"Ordering Rational Numbers\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_gx7H1O3vrdg\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_gx7H1O3vrdg\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_gx7H1O3vrdg\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction Orc_Function() {\n  var x = document.getElementById(\"Orc\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"Orc_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"Orc\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Rational_Number_Definition\" class=\"smooth-scroll\">Rational Number Definition<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Ordering_Rational_Numbers\" class=\"smooth-scroll\">Ordering Rational Numbers<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Ordering_Rational_Numbers_Practice_Questions\" class=\"smooth-scroll\">Ordering Rational Numbers Practice Questions<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label><input id=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hello, and welcome to this video on ordering rational numbers! This video will show you how to list rational numbers from least to greatest or greatest to least.<\/p>\n<h2><span id=\"Rational_Number_Definition\" class=\"m-toc-anchor\"><\/span>Rational Number Definition<\/h2>\n<p>\nFirst, let\u2019s review the definition of a <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/rational-numbers\/\">rational number<\/a>. A rational number is any number that can be turned into a fraction with an integer in both the numerator and the denominator. \\(\\frac{1}{4}\\) and \\(\\frac{9}{7}\\) are examples of rational numbers. It\u2019s also important to note that 0.25 and 25% are also rational numbers because they are equivalent to \\(\\frac{1}{4}\\) and therefore can be turned into a fraction that divides two integers.<\/p>\n<h2><span id=\"Ordering_Rational_Numbers\" class=\"m-toc-anchor\"><\/span>Ordering Rational Numbers<\/h2>\n<p>\nOne of the easiest ways to order rational numbers is to turn them all into decimals and then put them in order. If we want to turn a <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/converting-percentages-to-decimals-and-fractions\/\">percentage into a decimal<\/a>, all we do is turn the percent sign into a decimal point and move it two places to the left. So 13% becomes 0.13, and 213% becomes 2.13. Turning fractions into decimals is a little bit more challenging but still doable. <\/p>\n<p>To turn a fraction into a decimal, we first have to remember that the fraction bar means divide. This means that \\(\\frac{3}{4}\\) is really the same as \\(3\\div 4\\). So if we want to turn \\(\\frac{3}{4}\\) into a decimal, we simply use long division to divide \\(3\\div 4\\).<\/p>\n<p>4 can&#8217;t go into 3 at all, so we add a decimal point and put a 0. Since we added a decimal point here, we need to add it to the top as well. 4 goes into 30 seven times. \\(7\\times 4=28\\), so we write 28 and subtract, and we&#8217;re left with 2. We then add another 0 and bring it down. And then see 4 goes into 20 five times. \\(4\\times 5=20\\), and when we subtract we get 0.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/01\/Long-division-problem-ordering-rational-numbers.webp\" alt=\"Long division problem\" width=\"100.5\" height=\"186\" class=\"aligncenter size-full wp-image-240571\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/01\/Long-division-problem-ordering-rational-numbers.webp 670w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/01\/Long-division-problem-ordering-rational-numbers-162x300.webp 162w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/01\/Long-division-problem-ordering-rational-numbers-553x1024.webp 553w\" sizes=\"(max-width: 670px) 100vw, 670px\" \/><\/p>\n<p>So \\(\\frac{3}{4}=0.75\\).<\/p>\n<p>Remember, some decimals continue for a really long time or end up repeating, so in these cases it might be helpful to round to three or four decimal places. That should give you enough information to know where to place that number in a list.<\/p>\n<p>One other thing we need to look at is how to order square roots of numbers. You can turn them into decimals and order them that way, but that is usually pretty hard to do without a calculator. Another way is to recognize what two numbers the square root falls between. Let\u2019s look at an example so I can show you what I\u2019m talking about.<\/p>\n<div class=\"examplesentence\">\\(\\sqrt{41}\\)<\/div>\n<p>\n&nbsp;<br \/>\n41 is not a perfect square, so the way to estimate its square root is to find the two perfect squares on either side of it. The perfect square right below 41 is 36, and the one right above it is 49. Now, we know that the \\(\\sqrt{36}=6\\) and the \\(\\sqrt{49}=7\\). So the \\(\\sqrt{41}\\) has to fall somewhere between 6 and 7.<\/p>\n<p>Notice, this doesn\u2019t give you a specific answer of what the\\(\\sqrt{41}\\) is in decimal form, but it gives you a general location of where it would fall in a sequence of numbers, which is typically all that you need to put it in order.<\/p>\n<p>Now that we have reviewed how to order numbers, let\u2019s practice by putting this sequence of numbers in order from least to greatest:<\/p>\n<div class=\"examplesentence\">\\(87\\%\\),  \\(\\frac{2}{9}\\),  \\(\\sqrt{78}\\),  \\(\\frac{45}{4}\\), \\(6.743\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<br \/>\nWe are going to start by turning each of these into a decimal.<\/p>\n<p>Remember, to turn a percent into a decimal, simply change the percent sign to a decimal point and move it two places to the left, so \\(87\\%=0.87\\).<\/p>\n<p>We can figure out what \\(\\frac{2}{9}\\) is by dividing \\(2\\div 9\\). Remember, a fraction bar always means divide!<\/p>\n<p>So \\(2\\div 9\\): 9 goes into 2 zero times. So we add a decimal and put a 0; putting a decimal up here also. 9 goes into 20 two times. \\(9\\times 2=18\\), and then we subtract and get 2. If we add a 0 and bring it down we get 20. 9 goes into 20 two times; we get 18, subtract, and get 2.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/01\/Long-division-problem-2.webp\" alt=\"Long division problem\" width=\"100.5\" height=\"186\" class=\"aligncenter size-full wp-image-240574\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/01\/Long-division-problem-2.webp 670w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/01\/Long-division-problem-2-162x300.webp 162w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/01\/Long-division-problem-2-553x1024.webp 553w\" sizes=\"(max-width: 670px) 100vw, 670px\" \/><\/p>\n<p>Notice that when we divide we get \\(0.\\bar{2}\\), so for this exercise we will round to 0.222.<\/p>\n<div class=\"examplesentence\">\\(\\frac{2}{9}\\approx 0.222\\)<\/div>\n<p>\n&nbsp;<br \/>\nWhen we look at a square root, remember we want to look for the two perfect squares that the number falls between. 78 falls between the perfect squares 64 and 81, which are the squares of 8 and 9 respectively. So the \\(\\sqrt{78}\\) falls somewhere between 8 and 9.<\/p>\n<div class=\"examplesentence\">\\(8 &#60; \\sqrt{78} &#60; 9\\)<\/div>\n<p>\n&nbsp;<br \/>\nWe can find \\(\\frac{45}{4}\\) by dividing, just like we did with \\(\\frac{2}{9}\\).<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/01\/Long-division-problem-3.webp\" alt=\"Long division problem\" width=\"102.6\" height=\"278.7\" class=\"aligncenter size-full wp-image-240577\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/01\/Long-division-problem-3.webp 684w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/01\/Long-division-problem-3-110x300.webp 110w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/01\/Long-division-problem-3-377x1024.webp 377w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/01\/Long-division-problem-3-565x1536.webp 565w\" sizes=\"(max-width: 684px) 100vw, 684px\" \/><\/p>\n<p>So \\(\\frac{45}{4}=11.25\\).<\/p>\n<p>And 6.743 is already in decimal format, so we don\u2019t have to do anything with that number.<\/p>\n<p>Now, all we have to do is put them in order from least to greatest. Before I do this, let me erase some of our scratch work so we have more room. When we do this, we get:<\/p>\n<div class=\"examplesentence\">\\(0.222\\), \\(0.87\\), \\(6.743\\), \\(\\sqrt{78}\\), \\(11.25\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<br \/>\nNow, these aren\u2019t our original values, so to get our final answer, we have to change our decimal values back into their originals.<\/p>\n<div class=\"examplesentence\">\\(\\frac{2}{9}, 87\\%, 6.743, \\sqrt{78}, \\frac{45}{4}\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<br \/>\nIf you were asked to put these numbers in order from greatest to least, you would follow all the same steps except at the very end order them opposite to how we did it in this example, so \\(\\frac{45}{4}\\) would be first and \\(\\frac{2}{9}\\) would be last.<\/p>\n<p>And that\u2019s all there is to it! I hope this video on ordering rational numbers was helpful. Thanks for watching and happy studying!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Ordering_Rational_Numbers_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Ordering Rational Numbers Practice Questions<\/h2>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nOrder the following rational numbers from greatest to least:<\/p>\n<div class=\"yellow-math-quote\">2<sup>2<\/sup>, 40%, 4.53, \\(\\frac{19}{4}\\), \\(\\frac{25}{6}\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-1-1\">\\(\\frac{19}{4}\\), 4.53, \\(\\frac{25}{6}\\), 2<sup>2<\/sup>, 40%<\/div><div class=\"PQ\"  id=\"PQ-1-2\">40%, 2<sup>2<\/sup>, \\(\\frac{25}{6}\\), 4.53, \\(\\frac{19}{4}\\)<\/div><div class=\"PQ\"  id=\"PQ-1-3\">4.53, \\(\\frac{25}{6}\\), \\(\\frac{19}{4}\\), 40%, 2<sup>2<\/sup><\/div><div class=\"PQ\"  id=\"PQ-1-4\">\\(\\frac{25}{4}\\), \\(\\frac{19}{4}\\), 40%, 2<sup>2<\/sup>, 4.53<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>First, convert all rational numbers into decimals:<\/p>\n<ul>\n<li style=\"margin-bottom: 10px\">\\(2^2=2\\times2=4\\)<\/li>\n<li style=\"margin-bottom: 10px\">\\(40\\%=40\\div 100=0.40\\)<\/li>\n<li style=\"margin-bottom: 10px\">\\(4.53=4.53\\)<\/li>\n<li style=\"margin-bottom: 10px\">\\(\\frac{19}{4}=19\\div 4=4.75\\)<\/li>\n<li>\\(\\frac{25}{6}=25\\div 6=4.16\\)<\/li>\n<\/ul>\n<p>Next, compare each place value digit, working from left to right, and order the decimals from greatest to least:<\/p>\n<p style=\"text-align: center\">4.75, 4.53, 4.16, 4, 0.4<\/p>\n<p>Finally, replace each decimal with the corresponding rational number from the original list:<\/p>\n<p style=\"text-align: center\">\\(\\frac{19}{4}\\), 4.53, \\(\\frac{25}{6}\\), 2<sup>2<\/sup>, 40%<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nOrder the following rational numbers from least to greatest:<\/p>\n<div class=\"yellow-math-quote\">0.780, 72.5%, \\(\\frac{4}{5}\\), \\(\\sqrt{4}\\), \\(\\frac{3}{4}\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-2-1\">72.5%, \\(\\frac{3}{4}\\), 0.780, \\(\\frac{4}{5}\\), \\(\\sqrt{4}\\)<\/div><div class=\"PQ\"  id=\"PQ-2-2\">\\(\\frac{4}{5}\\), \\(\\sqrt{4}\\), 72.5%, \\(\\frac{3}{4}\\), 0.780<\/div><div class=\"PQ\"  id=\"PQ-2-3\">\\(\\sqrt{4}\\), 0.780, \\(\\frac{3}{4}\\), 72.5%, \\(\\frac{4}{5}\\)<\/div><div class=\"PQ\"  id=\"PQ-2-4\">\\(\\frac{3}{4}\\), \\(\\frac{4}{5}\\), \\(\\sqrt{4}\\), 0.780, 72.5%<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>First, convert all rational numbers into decimals:<\/p>\n<ul>\n<li style=\"margin-bottom: 10px\">\\(0.780=0.780\\)<\/li>\n<li style=\"margin-bottom: 10px\">\\(72.5\\%=72.5\\div100=0.725\\)<\/li>\n<li style=\"margin-bottom: 10px\">\\(\\frac{4}{5}=4\\div5=0.80\\)<\/li>\n<li style=\"margin-bottom: 10px\">\\(\\sqrt{4}=2\\)<\/li>\n<li>\\(\\frac{3}{4}=3\\div4=0.75\\)<\/li>\n<\/ul>\n<p>Next, compare each place value digit, working from left to right, and order the decimals from least to greatest:<\/p>\n<p style=\"text-align: center\">0.725, 0.75, 0.780, 0.80, 2<\/p>\n<p>Finally, replace each decimal with the corresponding rational number from the original list:<\/p>\n<p style=\"text-align: center\">72.5%, \\(\\frac{3}{4}\\), 0.780, \\(\\frac{4}{5}\\), \\(\\sqrt{4}\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhich of the following sets of rational numbers is ordered from least to greatest?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">\\(\\frac{3}{4}\\), 4, 4, 10<sup>1<\/sup>, 72%, 0.67<\/div><div class=\"PQ\"  id=\"PQ-3-2\">1.2, \\(\\frac{3}{4}\\), 50%, 1.25, \\(\\frac{11}{6}\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-3\">\\(\\frac{1}{2}\\), \\(\\frac{3}{4}\\), 80%, \\(frac{11}{2}\\), 6.85<\/div><div class=\"PQ\"  id=\"PQ-3-4\">\\(\\frac{3}{2}\\), 1.85, 85%, \\(\\frac{4}{9}\\), 91.5%<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>First, convert the rational numbers in all answer options into decimals:<\/p>\n<ol style=\"list-style-type: lower-alpha\">\n<li style=\"margin-bottom: 10px\">0.75, 4.4, 10, 0.72, 0.67<\/li>\n<li style=\"margin-bottom: 10px\">1.2, 0.75, 0.5, 1.25, 1.83<\/li>\n<li style=\"margin-bottom: 10px\">0.50, 0.75, 0.80, 5.5, 6.85<\/li>\n<li>1.5, 1.85, 0.85, 0.44, 0.915<\/li>\n<\/ol>\n<p>Next, compare the place value digits in each answer option, working from left to right. Finally, select the answer option with the decimals correctly ordered from least to greatest, which is C.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nA librarian is arranging books using the Dewey Decimal System. Which group of book numbers is correctly listed in order from least to greatest? <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">821.609, 821.53, 821.252, 821.2<\/div><div class=\"PQ\"  id=\"PQ-4-2\">821.252, 821.2, 821.609, 821.53<\/div><div class=\"PQ\"  id=\"PQ-4-3\">821.609, 821.2, 821.252, 821.53<\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-4\">821.2, 821.252, 821.53, 821.609<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>Compare each place value digit, working from left to right, and order the decimals from least to greatest. Since all numbers have the same values in the hundreds, tens, and ones place, start by comparing the digit in the tenths place.<\/p>\n<p>The digits in the tenths place for answer D are 2, 2, 5, and 6, which are ordered from least to greatest. Since the first two numbers have 2 in the tenths place, compare their hundredths place numbers, which are 0 and 5 respectively. Therefore, D is the correct answer. <\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nElizabeth is helping her teacher organize math tests for student portfolios. Other teachers in the math department helped score the tests, so not all grades look the same. Some are written as fractions, some as decimals, and some as percents:<\/p>\n<div class=\"yellow-math-quote\">87%, 0.8, \\(\\frac{24}{25}\\), \\(\\frac{16}{25}\\), 72%<\/div>\n<p>If Elizabeth\u2019s teacher tells her to order the tests from highest to lowest score, what is the correct order of test scores? <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">87%, 72%, \\(\\frac{24}{25}\\), \\(\\frac{16}{25}\\), 0.8<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-2\">\\(\\frac{24}{25}\\), 87%, 0.8, 72%, \\(\\frac{16}{25}\\)<\/div><div class=\"PQ\"  id=\"PQ-5-3\">0.8, \\(\\frac{16}{25}\\), \\(\\frac{24}{25}\\), 72%, 87%<\/div><div class=\"PQ\"  id=\"PQ-5-4\">\\(\\frac{16}{25}\\), 72%, 0.8, 87%, \\(\\frac{24}{25}\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>First, convert all rational numbers into decimals:<\/p>\n<ul>\n<li style=\"margin-bottom: 10px\">\\(87\\%=87\\div100=0.87\\)<\/li>\n<li style=\"margin-bottom: 10px\">\\(0.8=0.80\\)<\/li>\n<li style=\"margin-bottom: 10px\">\\(\\frac{24}{25}=0.96\\)<\/li>\n<li style=\"margin-bottom: 10px\">\\(\\frac{16}{25}=0.64\\)<\/li>\n<li>\\(72\\%=72\\div100=0.72\\)<\/li>\n<\/ul>\n<p>Next, compare each place value digit, working from left to right, and order the decimals from greatest to least:<\/p>\n<p style=\"text-align: center\">0.96, 0.87, 0.80. 0.72. 0.64<\/p>\n<p>Finally, replace each decimal with the corresponding rational number from the original list:<\/p>\n<p style=\"text-align: center\">\\(\\frac{24}{25}\\), 87%, 0.8, 72%, \\(\\frac{16}{25}\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/pre-algebra\/\">Return to Pre-Algebra Videos<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Return to Pre-Algebra Videos<\/p>\n","protected":false},"author":1,"featured_media":100372,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":{"0":"post-4504","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-math-advertising-group","7":"page_category-pre-algebra-numbers-videos","8":"page_category-pre-algebra-rational-numbers-videos","9":"page_category-video-pages-for-study-course-sidebar-ad","10":"page_type-video","11":"content_type-practice-questions","12":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/4504","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=4504"}],"version-history":[{"count":7,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/4504\/revisions"}],"predecessor-version":[{"id":280559,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/4504\/revisions\/280559"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/100372"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=4504"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}