Write 8\/11 as a recurring decimal<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To express ( \\frac{8}{11} ) as a recurring decimal, divide 8 by 11. The answer is:<\/p>\n\n\n\n [ where the “72” repeats indefinitely.<\/p>\n\n\n\n Write 8\/11 as a recurring decimal The Correct Answer and Explanation is : To express ( \\frac{8}{11} ) as a recurring decimal, divide 8 by 11. The answer is: [\\frac{8}{11} = 0.\\overline{72}] where the “72” repeats indefinitely. Explanation<\/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-163240","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/163240","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=163240"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/163240\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=163240"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=163240"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=163240"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\\frac{8}{11} = 0.\\overline{72}
]<\/p>\n\n\n\nExplanation<\/h3>\n\n\n\n
\n
To find the decimal form of ( \\frac{8}{11} ), we perform long division. Dividing 8 by 11, we see that 11 doesn\u2019t go into 8, so we place a decimal point and add a zero, making it 80. Now, 11 goes into 80 seven times (since (11 \\times 7 = 77)). Subtracting 77 from 80 leaves a remainder of 3.<\/li>\n\n\n\n
Bringing down another zero makes it 30. Dividing 30 by 11 gives us 2 (since (11 \\times 2 = 22)). Subtracting 22 from 30 leaves a remainder of 8, bringing us back to the beginning. Now, 80 divided by 11 gives 7, repeating the process.<\/li>\n\n\n\n
This cycle \u2014 where 7 and 2 keep appearing \u2014 will continue indefinitely. As such, the decimal representation of ( \\frac{8}{11} ) is ( 0.\\overline{72} ), with “72” as the repeating block.<\/li>\n\n\n\n
Since 11 is a prime number and does not divide evenly into 100, the division produces a repeating decimal rather than terminating. For a fraction to have a terminating decimal, its denominator (in simplest form) must contain only the prime factors 2 or 5. Because 11 doesn\u2019t meet this condition, ( \\frac{8}{11} ) results in a recurring decimal.<\/li>\n\n\n\n
The result ( 0.\\overline{72} ) accurately represents ( \\frac{8}{11} ) in decimal form.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"