{"id":244278,"date":"2025-07-05T03:24:04","date_gmt":"2025-07-05T03:24:04","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=244278"},"modified":"2025-07-05T03:24:06","modified_gmt":"2025-07-05T03:24:06","slug":"true-or-false-8","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/05\/true-or-false-8\/","title":{"rendered":"True or False"},"content":{"rendered":"\n

True or False: 0.33333 . . . is a rational number.<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

True<\/strong>.<\/p>\n\n\n\n

The number 0.33333\u20260.33333 \\dots0.33333\u2026 (with the threes repeating indefinitely) is a rational number<\/strong>. To understand why, let’s break it down:<\/p>\n\n\n\n

    \n
  1. Definition of Rational Numbers<\/strong>: A rational number is any number that can be expressed as the fraction of two integers, i.e., in the form pq\\frac{p}{q}qp\u200b, where ppp and qqq are integers and q\u22600q \\neq 0q\ue020=0. Rational numbers can be written as either terminating or repeating decimals.<\/li>\n\n\n\n
  2. Repeating Decimals<\/strong>: The decimal 0.33333\u20260.33333 \\dots0.33333\u2026 is an example of a repeating decimal<\/strong>. Specifically, it is a repeating decimal with the digit “3” repeating indefinitely. Repeating decimals are always rational because they can be written as a fraction.<\/li>\n\n\n\n
  3. Converting to a Fraction<\/strong>: You can convert 0.33333\u20260.33333 \\dots0.33333\u2026 to a fraction using a simple algebraic method. Let x=0.33333\u2026x = 0.33333 \\dotsx=0.33333\u2026. To eliminate the repeating decimal, multiply both sides of the equation by 10: 10x=3.33333\u202610x = 3.33333 \\dots10x=3.33333\u2026 Subtract the original equation x=0.33333\u2026x = 0.33333 \\dotsx=0.33333\u2026 from this: 10x\u2212x=3.33333\u22ef\u22120.33333\u202610x – x = 3.33333 \\dots – 0.33333 \\dots10x\u2212x=3.33333\u22ef\u22120.33333\u2026 9x=39x = 39x=3 x=39=13x = \\frac{3}{9} = \\frac{1}{3}x=93\u200b=31\u200b<\/li>\n\n\n\n
  4. Conclusion<\/strong>: The decimal 0.33333\u20260.33333 \\dots0.33333\u2026 is equivalent to the fraction 13\\frac{1}{3}31\u200b, which is a ratio of two integers. Hence, 0.33333\u20260.33333 \\dots0.33333\u2026 is a rational number.<\/li>\n<\/ol>\n\n\n\n

    In summary, any repeating decimal can be expressed as a fraction, making it a rational number. Therefore, the statement that 0.33333\u20260.33333 \\dots0.33333\u2026 is a rational number is True<\/strong>.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    True or False: 0.33333 . . . is a rational number. The Correct Answer and Explanation is: True. The number 0.33333\u20260.33333 \\dots0.33333\u2026 (with the threes repeating indefinitely) is a rational number. To understand why, let’s break it down: In summary, any repeating decimal can be expressed as a fraction, making it a rational number. Therefore, […]<\/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-244278","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/244278","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=244278"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/244278\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=244278"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=244278"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=244278"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}