{"id":277073,"date":"2025-07-31T10:26:22","date_gmt":"2025-07-31T10:26:22","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=277073"},"modified":"2025-07-31T10:26:25","modified_gmt":"2025-07-31T10:26:25","slug":"which-number-is-rational","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/31\/which-number-is-rational\/","title":{"rendered":"Which number is rational"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/image-1367.png\" alt=\"\" class=\"wp-image-277074\"\/><\/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 correct answer is&nbsp;<strong>D. 0.333&#8230;<\/strong><\/p>\n\n\n\n<p>A rational number is defined as any number that can be expressed as a fraction, or ratio, of two integers (p\/q), where the denominator (q) is not zero. The decimal representation of a rational number will either terminate, meaning it ends, or it will repeat in a predictable pattern forever.<\/p>\n\n\n\n<p>Let&#8217;s analyze each option based on this definition:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>A. \u03c0 (pi):<\/strong>\u00a0Pi is a famous irrational number. Its decimal representation (3.14159&#8230;) continues infinitely without ever repeating a pattern. Therefore, it cannot be written as a simple fraction and is not rational.<\/li>\n\n\n\n<li><strong>B. 0.83587643&#8230;:<\/strong>\u00a0The ellipsis (&#8230;) indicates that the decimal continues. However, there is no discernible repeating pattern in the digits shown. In mathematics problems of this type, a number presented this way is intended to represent a non-terminating, non-repeating decimal, which is the definition of an irrational number.<\/li>\n\n\n\n<li><strong>C. \u221a7 (the square root of 7):<\/strong>\u00a0The square root of any integer that is not a perfect square is an irrational number. Since 7 is not a perfect square (like 4 or 9), its square root results in a decimal that goes on forever with no repeating pattern (approximately 2.64575&#8230;). Thus, it is irrational.<\/li>\n\n\n\n<li><strong>D. 0.333&#8230;:<\/strong>\u00a0This number is a repeating decimal. The digit &#8216;3&#8217; repeats infinitely, as indicated by the ellipsis. All repeating decimals are rational because they can be converted into a fraction. The number 0.333&#8230; is the decimal representation of the fraction 1\/3. Since it can be expressed as a ratio of two integers (1 and 3), it perfectly fits the definition of a rational number.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-2686.jpeg\" alt=\"\" class=\"wp-image-277075\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The Correct Answer and Explanation is: The correct answer is&nbsp;D. 0.333&#8230; A rational number is defined as any number that can be expressed as a fraction, or ratio, of two integers (p\/q), where the denominator (q) is not zero. The decimal representation of a rational number will either terminate, meaning it ends, or it will [&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-277073","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/277073","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=277073"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/277073\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=277073"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=277073"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=277073"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}