{"id":243978,"date":"2025-07-04T18:17:43","date_gmt":"2025-07-04T18:17:43","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=243978"},"modified":"2025-07-04T18:17:45","modified_gmt":"2025-07-04T18:17:45","slug":"what-is-1-21-repeating-as-a-fraction-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/04\/what-is-1-21-repeating-as-a-fraction-2\/","title":{"rendered":"What is 1.21 repeating as a fraction"},"content":{"rendered":"\n

What is 1.21 repeating as a fraction?<\/p>\n\n\n\n

The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To convert the repeating decimal 1.2121\u203e1.21\\overline{21} into a fraction, follow these steps:<\/p>\n\n\n\n

    \n
  1. Represent the number algebraically<\/strong>: Let x=1.2121\u203ex = 1.21\\overline{21}. This means that the digits “21” repeat indefinitely after the decimal point.<\/li>\n\n\n\n
  2. Remove the repeating decimal<\/strong>: To eliminate the repeating part, multiply both sides of the equation by 100. This gives: 100x=121.2121\u203e100x = 121.21\\overline{21} Notice that the decimal part of both xx and 100x100x is the same (i.e., 0.21\\overline{21}).<\/li>\n\n\n\n
  3. Subtract the original equation from this new equation<\/strong>: Subtract the equation x=1.2121\u203ex = 1.21\\overline{21} from 100x=121.2121\u203e100x = 121.21\\overline{21}: 100x\u2212x=121.2121\u203e\u22121.2121\u203e100x – x = 121.21\\overline{21} – 1.21\\overline{21} This simplifies to: 99x=12099x = 120<\/li>\n\n\n\n
  4. Solve for xx<\/strong>: Now divide both sides of the equation by 99 to isolate xx: x=12099x = \\frac{120}{99}<\/li>\n\n\n\n
  5. Simplify the fraction<\/strong>: To simplify the fraction, find the greatest common divisor (GCD) of 120 and 99. The GCD is 3. Divide both the numerator and denominator by 3: x=120\u00f7399\u00f73=4033x = \\frac{120 \\div 3}{99 \\div 3} = \\frac{40}{33}<\/li>\n<\/ol>\n\n\n\n

    Thus, 1.2121\u203e1.21\\overline{21} as a fraction is 4033\\frac{40}{33}.<\/p>\n\n\n\n

    This process works because multiplying by powers of 10 shifts the decimal point, and subtracting removes the repeating part, leaving a solvable equation.<\/p>\n","protected":false},"excerpt":{"rendered":"

    What is 1.21 repeating as a fraction? The correct answer and explanation is: To convert the repeating decimal 1.2121\u203e1.21\\overline{21} into a fraction, follow these steps: Thus, 1.2121\u203e1.21\\overline{21} as a fraction is 4033\\frac{40}{33}. This process works because multiplying by powers of 10 shifts the decimal point, and subtracting removes the repeating part, leaving a solvable equation.<\/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-243978","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/243978","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=243978"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/243978\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=243978"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=243978"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=243978"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}