{"id":258907,"date":"2025-07-18T14:56:54","date_gmt":"2025-07-18T14:56:54","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=258907"},"modified":"2025-07-18T14:56:56","modified_gmt":"2025-07-18T14:56:56","slug":"what-is-0-63-repeating-expressed-as-a-fraction-in-simplest-form","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/18\/what-is-0-63-repeating-expressed-as-a-fraction-in-simplest-form\/","title":{"rendered":"What is 0.63 repeating expressed as a fraction in simplest form"},"content":{"rendered":"\n

What is 0.63 repeating expressed as a fraction in simplest form?<\/p>\n\n\n\n

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

To express 0.63 repeating as a fraction, follow these steps:<\/p>\n\n\n\n

Step 1: Let x=0.63\u203ex = 0.\\overline{63}x=0.63<\/h3>\n\n\n\n

This means the decimal is repeating every two digits (63). So, we can set up the equation: x=0.6363636363\u2026x = 0.6363636363\\ldotsx=0.6363636363\u2026<\/p>\n\n\n\n

Step 2: Eliminate the repeating decimal<\/h3>\n\n\n\n

Multiply both sides of the equation by 100. This shifts the decimal point two places to the right: 100x=63.6363636363\u2026100x = 63.6363636363\\ldots100x=63.6363636363\u2026<\/p>\n\n\n\n

Now we have two equations:<\/p>\n\n\n\n

    \n
  1. x=0.6363636363\u2026x = 0.6363636363\\ldotsx=0.6363636363\u2026<\/li>\n\n\n\n
  2. 100x=63.6363636363\u2026100x = 63.6363636363\\ldots100x=63.6363636363\u2026<\/li>\n<\/ol>\n\n\n\n

    Step 3: Subtract the first equation from the second<\/h3>\n\n\n\n

    Now subtract x=0.6363636363\u2026x = 0.6363636363\\ldotsx=0.6363636363\u2026 from 100x=63.6363636363\u2026100x = 63.6363636363\\ldots100x=63.6363636363\u2026: 100x\u2212x=63.6363636363\u2026\u22120.6363636363\u2026100x – x = 63.6363636363\\ldots – 0.6363636363\\ldots100x\u2212x=63.6363636363\u2026\u22120.6363636363\u2026<\/p>\n\n\n\n

    Simplifying both sides: 99x=6399x = 6399x=63<\/p>\n\n\n\n

    Step 4: Solve for xxx<\/h3>\n\n\n\n

    Now, divide both sides by 99 to isolate xxx: x=6399x = \\frac{63}{99}x=9963\u200b<\/p>\n\n\n\n

    Step 5: Simplify the fraction<\/h3>\n\n\n\n

    We can simplify 6399\\frac{63}{99}9963\u200b by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 63 and 99 is 9. So, divide both by 9: 63\u00f7999\u00f79=711\\frac{63 \\div 9}{99 \\div 9} = \\frac{7}{11}99\u00f7963\u00f79\u200b=117\u200b<\/p>\n\n\n\n

    Thus, the decimal 0.63\u203e0.\\overline{63}0.63 is equivalent to the fraction 711\\frac{7}{11}117\u200b.<\/p>\n\n\n\n

    Final Answer:<\/h3>\n\n\n\n

    The repeating decimal 0.63\u203e0.\\overline{63}0.63 is expressed as the fraction 711\\frac{7}{11}117\u200b.<\/p>\n\n\n\n

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

    What is 0.63 repeating expressed as a fraction in simplest form? The Correct Answer and Explanation is: To express 0.63 repeating as a fraction, follow these steps: Step 1: Let x=0.63\u203ex = 0.\\overline{63}x=0.63 This means the decimal is repeating every two digits (63). So, we can set up the equation: x=0.6363636363\u2026x = 0.6363636363\\ldotsx=0.6363636363\u2026 Step 2: […]<\/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-258907","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/258907","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=258907"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/258907\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=258907"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=258907"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=258907"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}