{"id":278764,"date":"2025-08-02T10:53:16","date_gmt":"2025-08-02T10:53:16","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=278764"},"modified":"2025-08-02T10:53:18","modified_gmt":"2025-08-02T10:53:18","slug":"name-the-rational-numbers-from-the-list-below","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/08\/02\/name-the-rational-numbers-from-the-list-below\/","title":{"rendered":"Name the rational numbers from the list below"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/08\/image-170.png\" alt=\"\" class=\"wp-image-278765\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The rational numbers from the list are:&nbsp;<strong>-20, 0, 36, 7.71, \u221a100, 7 1\/2, and -2\/39.<\/strong><\/p>\n\n\n\n<p>A rational number is a number that can be expressed as a fraction or quotient, p\/q, where p and q are both integers and the denominator, q, is not zero. To determine which numbers from the list fit this definition, we can examine each one individually.<\/p>\n\n\n\n<p>First, we consider the integers in the list: -20, 0, and 36. All integers are rational because they can be written as a fraction with a denominator of 1. For example, -20 can be written as -20\/1, 0 can be written as 0\/1, and 36 can be written as 36\/1. Since they all fit the p\/q format, they are rational.<\/p>\n\n\n\n<p>Next, we look at the decimal 7.71. This is a terminating decimal, meaning it has a finite number of digits after the decimal point. All terminating decimals are rational because they can be converted into a fraction with a power of ten in the denominator. The number 7.71 is equivalent to the fraction 771\/100, which is a ratio of two integers. Therefore, 7.71 is a rational number.<\/p>\n\n\n\n<p>The number \u221a100 is the square root of 100. Since 100 is a perfect square (10 \u00d7 10 = 100), the square root of 100 simplifies to the integer 10. As we have already established, all integers are rational, so \u221a100 is a rational number.<\/p>\n\n\n\n<p>The mixed number 7 1\/2 can be converted into an improper fraction. By multiplying the whole number by the denominator and adding the numerator, we get (7 \u00d7 2) + 1 = 15. The improper fraction is 15\/2. This is a ratio of two integers, so 7 1\/2 is rational.<\/p>\n\n\n\n<p>The number -2\/39 is already presented in the form of a fraction with an integer numerator (-2) and a non-zero integer denominator (39), directly fitting the definition of a rational number.<\/p>\n\n\n\n<p>The remaining numbers, \u221a13 and \u03c0, are irrational. The number 13 is not a perfect square, so its square root results in a non-terminating, non-repeating decimal, which cannot be written as a simple fraction. Pi (\u03c0) is a famous transcendental number whose decimal representation also continues forever without repeating. Thus, these two numbers are not rational.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/08\/learnexams-banner6-46.jpeg\" alt=\"\" class=\"wp-image-278770\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The Correct Answer and Explanation is: The rational numbers from the list are:&nbsp;-20, 0, 36, 7.71, \u221a100, 7 1\/2, and -2\/39. A rational number is a number that can be expressed as a fraction or quotient, p\/q, where p and q are both integers and the denominator, q, is not zero. To determine which numbers [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-278764","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/278764","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=278764"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/278764\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=278764"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=278764"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=278764"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}