{"id":13129,"date":"2014-02-07T17:03:48","date_gmt":"2014-02-07T17:03:48","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=13129"},"modified":"2026-03-28T11:08:33","modified_gmt":"2026-03-28T16:08:33","slug":"irrational-numbers-on-a-number-line","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/irrational-numbers-on-a-number-line\/","title":{"rendered":"Irrational Numbers on a Number Line"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_t1oLS6jnjMA\" 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_t1oLS6jnjMA\" data-source-videoID=\"t1oLS6jnjMA\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Irrational Numbers on a Number Line Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Irrational Numbers on a Number Line\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_t1oLS6jnjMA:hover {cursor:pointer;} img#videoThumbnailImage_t1oLS6jnjMA {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/1207-irrational-numbers-on-a-number-line-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_t1oLS6jnjMA\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_t1oLS6jnjMA\" 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\",\"Irrational Numbers on a Number Line\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_t1oLS6jnjMA\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_t1oLS6jnjMA\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_t1oLS6jnjMA\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction KMJ_Function() {\n  var x = document.getElementById(\"KMJ\");\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=\"KMJ_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=\"KMJ\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Irrational_Numbers\" class=\"smooth-scroll\">Irrational Numbers<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Rational_Numbers\" class=\"smooth-scroll\">Rational Numbers<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Irrational_Numbers_on_a_Number_Line\" class=\"smooth-scroll\">Irrational Numbers on a Number Line<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Irrational_Number_Practice_Questions\" class=\"smooth-scroll\">Irrational Number 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>Hi, and welcome to this review of irrational numbers! Today, we\u2019ll be reminded of what an irrational number is, and look at where they fall on a <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/real-numbers-and-the-number-line\/\">number line<\/a>. Let\u2019s get started!<\/p>\n<h2><span id=\"Irrational_Numbers\" class=\"m-toc-anchor\"><\/span>Irrational Numbers<\/h2>\n<p>\nSo, first, what is an irrational number? It is easy to determine whether a number is rational or irrational based on the word itself.  Look closely\u2026 the root word ratio tells us that these numbers can be written as a fraction.<\/p>\n<h2><span id=\"Rational_Numbers\" class=\"m-toc-anchor\"><\/span>Rational Numbers<\/h2>\n<p>\nRational numbers include all proper and improper <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/fractions\/\">fractions<\/a>.  Decimals that repeat or that terminate can be written as fractions, so they are considered rational. For example, .3333333 can be expressed as the fraction, 13, so it is a rational number.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-114065 aligncenter\" style=\"box-shadow: 1.5px 1.5px 3px grey;\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/02\/Number-classification.png\" alt=\"Examples of rational and irrational numbers, integers, and whole numbers\" width=\"653\" height=\"303\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/02\/Number-classification.png 653w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/02\/Number-classification-300x139.png 300w\" sizes=\"auto, (max-width: 653px) 100vw, 653px\" \/><\/p>\n<p>This diagram clearly shows that there is no overlap between the rational and irrational number sets.  Another way of thinking about it is that irrational numbers are those that cannot be written as a fraction. <\/p>\n<p>A common example of an irrational number is the value derived from taking the square root of a non-perfect square.  That may sound confusing, so let\u2019s look at a few examples to simplify the terminology.<\/p>\n<p>A <strong>perfect square<\/strong> is a number that can be re-written as an integer multiplied by itself.  <br \/>\nFor example,  \\(4 = 2 \\times 2\\), or written another way, \\(4 = 2^2\\).  This shows that 4 is a perfect square.  <\/p>\n<p>Similarly, 16 can be rewritten as \\(4 \\times 4\\), or \\(4^2\\).  So, 16 is also a perfect square. <\/p>\n<h2><span id=\"Irrational_Numbers_on_a_Number_Line\" class=\"m-toc-anchor\"><\/span>Irrational Numbers on a Number Line<\/h2>\n<p>\nBecause taking the square root of a perfect square results in an integer, it can easily be found on a number line. But how do we know where the value \\(\\sqrt5\\) would fall on a number line?  Well, \\(\\sqrt{5}\\) = 2.236, so we can guess that it lands somewhere around here on the number line.<\/p>\n<p>Let\u2019s say we had \\(\\sqrt{31}\\). Where would this value fall on a number line?<\/p>\n<p>Thirty-one is not a perfect square.  The closest perfect square that is less than 31 is 25, and the closest perfect square greater than 31 is 36.  The square roots of 25 and 36 are 5 and 6, respectively, so we know we can place \\(\\sqrt{31}\\) somewhere in between. If we calculate \\(\\sqrt{31}\\), we indeed get 5.567, so we can estimate that it falls halfway between 5 and 6.<\/p>\n<p>There are actually some famous irrational numbers that you may have seen before.  Pi, for example, is a non-repeating decimal that goes on for infinity every time\u2026 for every circle!  When calculating with pi, a common estimate is 3.14159, or the fraction \\(\\frac{22}{7}\\).  <\/p>\n<p>Phi is another irrational number that can, at best, be mathematically approximated.  The general estimation is the value 1.618, which is used in visual arts, architecture, and design applications.  <\/p>\n<p>The math constant, <em>e<\/em>, is seen frequently in math, and is estimated with the value of 2.71828.  This special irrational number is sometimes referred to as Euler\u2019s Number to credit the Swiss mathematician, Leonhard Euler.  Formulas dealing with natural logs, complex numbers, and advanced concepts in calculus all use this important irrational number.<\/p>\n<p>So, as you can see, irrational numbers are unique in that they cannot be expressed fully as fractions, but they can be visualized on a number line with rational numbers by using approximations.<\/p>\n<p>Thanks for watching, and happy studying!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Irrational_Number_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Irrational Number 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 \/>\nIs the number \\(2\\pi\\) a rational or irrational number? Represent this value using a number line.<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">Rational<br>\r\n<img decoding=\"async\" class=\" wp-image-72151 alignnone\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-between-6-and-7-but-closer-to-6.png\" alt=\"number line in one unit increments from 5 to 8, red dot between 6 and 7 but closer to 6\" width=\"337.45\" height=\"78.2\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-between-6-and-7-but-closer-to-6.png 1280w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-between-6-and-7-but-closer-to-6-300x70.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-between-6-and-7-but-closer-to-6-1024x238.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-between-6-and-7-but-closer-to-6-768x178.png 768w\" sizes=\"(max-width: 1280px) 100vw, 1280px\" \/><\/div><div class=\"PQ\"  id=\"PQ-1-2\">Irrational<br>\r\n<img decoding=\"async\" class=\" wp-image-72148 alignnone\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-on-6.png\" alt=\"number line in one unit increments from 5 to 8, red dot on 6\" width=\"337.45\" height=\"78.2\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-on-6.png 1280w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-on-6-300x70.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-on-6-1024x238.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-on-6-768x178.png 768w\" sizes=\"(max-width: 1280px) 100vw, 1280px\" \/><\/div><div class=\"PQ\"  id=\"PQ-1-3\">Rational<br>\r\n<img decoding=\"async\" class=\" wp-image-72148 alignnone\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-on-6.png\" alt=\"number line in one unit increments from 5 to 8, red dot on 6\" width=\"337.45\" height=\"78.2\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-on-6.png 1280w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-on-6-300x70.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-on-6-1024x238.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-on-6-768x178.png 768w\" sizes=\"(max-width: 1280px) 100vw, 1280px\" \/><\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-4\">Irrational<br>\r\n<img decoding=\"async\" class=\" wp-image-72151 alignnone\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-between-6-and-7-but-closer-to-6.png\" alt=\"number line in one unit increments from 5 to 8, red dot between 6 and 7 but closer to 6\" width=\"337.45\" height=\"78.2\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-between-6-and-7-but-closer-to-6.png 1280w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-between-6-and-7-but-closer-to-6-300x70.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-between-6-and-7-but-closer-to-6-1024x238.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-between-6-and-7-but-closer-to-6-768x178.png 768w\" sizes=\"(max-width: 1280px) 100vw, 1280px\" \/><\/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>We know that \\(\\pi\\) is an irrational number because it can\u2019t be written as a fraction with whole numbers in both the numerator and denominator, so \\(2\\pi\\) is an irrational number as well. Additionally, the value \\(2\\pi \\approx 6.28318\\) sits between 6 and 7.<\/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 \/>\nFind the two consecutive integers that \\(\\sqrt{77}\\) sits between and build the inequality.<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">\\(\\sqrt{76} \\lt \\sqrt{77} \\lt \\sqrt{78}\\)<\/div><div class=\"PQ\"  id=\"PQ-2-2\">\\(1 \\lt \\sqrt{77} \\lt 10\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-3\">\\(8 \\lt \\sqrt{77} \\lt 9\\)<\/div><div class=\"PQ\"  id=\"PQ-2-4\">\\(7 \\lt \\sqrt{77} \\lt 9\\)<\/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>To find which two consecutive integers \\(\\sqrt{77}\\) falls between, look for the perfect squares closest to 77. Since \\(8^2=64\\) and \\(9^2=81\\), and since \\(64 \\lt 77 \\lt 81\\), taking the square root shows:<\/p>\n<p style=\"text-align: center\">\\(8 \\lt \\sqrt{77} \\lt 9\\)<\/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 \/>\nFind the two consecutive integers that border \\(2\\sqrt{14}\\) and build the inequality.<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-3-1\">\\(7 \\lt 2 \\sqrt{14} \\lt 8\\)<\/div><div class=\"PQ\"  id=\"PQ-3-2\">\\(14 \\lt \\sqrt{14} \\lt 15\\)<\/div><div class=\"PQ\"  id=\"PQ-3-3\">\\(6 \\lt 2\\sqrt{14} \\lt 8\\)<\/div><div class=\"PQ\"  id=\"PQ-3-4\">\\(3 \\lt 2\\sqrt{14} \\lt 4\\)<\/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>To find which two consecutive integers \\(2 \\sqrt{14}\\) falls between, first rewrite it as a single square root:<\/p>\n<p style=\"text-align: center\">\\(2 \\sqrt{14} = \\sqrt{56}\\)<\/p>\n<p>Now find the perfect squares closest to 56.<\/p>\n<p>Since \\(7^2=49\\) and \\(8^2=64\\), and since \\(49 \\lt 56 \\lt 64\\), taking the square root gives:<\/p>\n<p style=\"text-align: center\">\\(7 \\lt \\sqrt{56} \\lt 8\\)<\/p>\n<p>Therefore, \\(7 \\lt 2\\sqrt{14} \\lt 8\\).<\/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>Represent the irrational number <span style=\"font-size: 120%\">\\(\\frac{26.7}{7.21}\\)<\/span> on a number line.<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\"><img decoding=\"async\" class=\" wp-image-72145 alignnone\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-1-to-4-red-dot-on-3.png\" alt=\"number line in one unit increments from 1 to 4, red dot on 3\" width=\"337.45\" height=\"78.2\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-1-to-4-red-dot-on-3.png 1280w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-1-to-4-red-dot-on-3-300x70.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-1-to-4-red-dot-on-3-1024x238.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-1-to-4-red-dot-on-3-768x178.png 768w\" sizes=\"(max-width: 1280px) 100vw, 1280px\" \/><\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-2\"><img decoding=\"async\" class=\" wp-image-72142 alignnone\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-1-to-4-red-dot-between-3-and-4-but-closer-to-4.png\" alt=\"number line in one unit increments from 1 to 4, red dot between 3 and 4 but closer to 4\" width=\"337.45\" height=\"78.2\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-1-to-4-red-dot-between-3-and-4-but-closer-to-4.png 1280w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-1-to-4-red-dot-between-3-and-4-but-closer-to-4-300x70.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-1-to-4-red-dot-between-3-and-4-but-closer-to-4-1024x238.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-1-to-4-red-dot-between-3-and-4-but-closer-to-4-768x178.png 768w\" sizes=\"(max-width: 1280px) 100vw, 1280px\" \/>\r\n<\/div><div class=\"PQ\"  id=\"PQ-4-3\"><img decoding=\"async\" class=\" wp-image-72139 alignnone\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-1-to-4-red-dot-on-4.png\" alt=\"number line in one unit increments from 1 to 4, red dot on 4\" width=\"337.45\" height=\"78.2\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-1-to-4-red-dot-on-4.png 1280w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-1-to-4-red-dot-on-4-300x69.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-1-to-4-red-dot-on-4-1024x237.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-1-to-4-red-dot-on-4-768x178.png 768w\" sizes=\"(max-width: 1280px) 100vw, 1280px\" \/>\r\n<\/div><div class=\"PQ\"  id=\"PQ-4-4\"><img decoding=\"async\" class=\" wp-image-72136 alignnone\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-negative-4-to-negative-1-red-dot-between-negative-4-and-negative-3-close-to-midway-but-slightly-closer-to-negative-4.png\" alt=\"number line in one unit increments from negative 4 to negative 1, red dot between negative 4 and negative 3, close to midway but slightly closer to negative 4\" width=\"337.45\" height=\"78.2\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-negative-4-to-negative-1-red-dot-between-negative-4-and-negative-3-close-to-midway-but-slightly-closer-to-negative-4.png 1280w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-negative-4-to-negative-1-red-dot-between-negative-4-and-negative-3-close-to-midway-but-slightly-closer-to-negative-4-300x70.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-negative-4-to-negative-1-red-dot-between-negative-4-and-negative-3-close-to-midway-but-slightly-closer-to-negative-4-1024x238.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-negative-4-to-negative-1-red-dot-between-negative-4-and-negative-3-close-to-midway-but-slightly-closer-to-negative-4-768x178.png 768w\" sizes=\"(max-width: 1280px) 100vw, 1280px\" \/>\r\n<\/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>To place the fraction on a number line, the first step is to estimate its value by comparing it to nearby multiples of 7.21.<\/p>\n<p>Since \\(7.21 \\times 3 = 21.63\\) and \\(7.21 \\times 4 = 28.84\\), and since 26.7 is between 21.63 and 28.84, we know that:<\/p>\n<p style=\"text-align: center\">\\(3 \\lt \\dfrac{26.7}{7.21} \\lt 4\\)<\/p>\n<p>This means that the point should be placed between 3 and 4 on the number line, closer to 4.<\/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 \/>\nRepresent the irrational number <span style=\"font-size: 120%\">\\(\\frac{5e}{2}\\)<\/span> on a number line.<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\"><img decoding=\"async\" class=\" wp-image-72133 alignnone\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-halfway-between-5-and-6.png\" alt=\"number line in one unit increments from 5 to 8, red dot halfway between 5 and 6\" width=\"337.45\" height=\"78.2\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-halfway-between-5-and-6.png 1280w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-halfway-between-5-and-6-300x69.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-halfway-between-5-and-6-1024x237.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-halfway-between-5-and-6-768x178.png 768w\" sizes=\"(max-width: 1280px) 100vw, 1280px\" \/><\/div><div class=\"PQ\"  id=\"PQ-5-2\"><img decoding=\"async\" class=\" wp-image-72148 alignnone\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-on-6.png\" alt=\"number line in one unit increments from 5 to 8, red dot on 6\" width=\"337.45\" height=\"78.2\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-on-6.png 1280w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-on-6-300x70.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-on-6-1024x238.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-on-6-768x178.png 768w\" sizes=\"(max-width: 1280px) 100vw, 1280px\" \/><\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-3\"><img decoding=\"async\" class=\" wp-image-72130 alignnone\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-between-6-and-7-but-closer-to-7.png\" alt=\"number line in one unit increments from 5 to 8, red dot between 6 and 7 but closer to 7\" width=\"337.45\" height=\"78.2\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-between-6-and-7-but-closer-to-7.png 1280w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-between-6-and-7-but-closer-to-7-300x70.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-between-6-and-7-but-closer-to-7-1024x238.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-between-6-and-7-but-closer-to-7-768x178.png 768w\" sizes=\"(max-width: 1280px) 100vw, 1280px\" \/><\/div><div class=\"PQ\"  id=\"PQ-5-4\"><img decoding=\"async\" class=\" wp-image-72127 alignnone\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-on-7.png\" alt=\"number line in one unit increments from 5 to 8, red dot on 7\" width=\"337.45\" height=\"78.2\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-on-7.png 1280w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-on-7-300x70.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-on-7-1024x238.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/number-line-in-one-unit-increments-from-5-to-8-red-dot-on-7-768x178.png 768w\" sizes=\"(max-width: 1280px) 100vw, 1280px\" \/><\/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>Plugging this value into a calculator will result in 6.7957, which would graph the point between 6 and 7.<\/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\/complex-arithmetic\/\">Return to Complex Arithmetic Videos<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Return to Complex Arithmetic Videos<\/p>\n","protected":false},"author":1,"featured_media":100315,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":{"0":"post-13129","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-exponents-and-radicals-complex-arithmetic-videos","7":"page_category-math-advertising-group","8":"page_category-pre-algebra-numbers-videos","9":"page_type-video","10":"content_type-practice-questions","11":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/13129","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=13129"}],"version-history":[{"count":6,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/13129\/revisions"}],"predecessor-version":[{"id":280820,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/13129\/revisions\/280820"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/100315"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=13129"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}