{"id":152484,"date":"2024-10-11T10:29:29","date_gmt":"2024-10-11T10:29:29","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=152484"},"modified":"2024-10-11T10:29:31","modified_gmt":"2024-10-11T10:29:31","slug":"what-is-0-12-repeating-expressed-as-a-fraction-in-simplest-form","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/11\/what-is-0-12-repeating-expressed-as-a-fraction-in-simplest-form\/","title":{"rendered":"What is 0.12 repeating expressed as a fraction in simplest form"},"content":{"rendered":"\n<p>What is 0.12 repeating expressed as a fraction in simplest form<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>The correct answer is: <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-3-color\"><strong>( \\frac{4}{33} )<\/strong><\/mark><\/p>\n\n\n\n<p>To express the repeating decimal ( 0.12\\overline{12} ) as a fraction, we can follow a systematic approach using algebra.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Define the Decimal<\/strong>: Let ( x = 0.12\\overline{12} ). This means ( x = 0.12121212\u2026 )<\/li>\n\n\n\n<li><strong>Eliminate the Repetition<\/strong>: To isolate the repeating part, we multiply both sides of the equation by 100 (since the repeat cycle has two digits). Thus:<br>[<br>100x = 12.121212\u2026<br>]<\/li>\n\n\n\n<li><strong>Set Up the Equation<\/strong>: We now have two equations:<br>[<br>x = 0.121212\u2026<br>]<br>[<br>100x = 12.121212\u2026<br>]<\/li>\n\n\n\n<li><strong>Subtract the Two Equations<\/strong>: Subtract the first equation from the second to eliminate the repeating part:<br>[<br>100x &#8211; x = 12.121212\u2026 &#8211; 0.121212\u2026<br>]<br>This simplifies to:<br>[<br>99x = 12<br>]<\/li>\n\n\n\n<li><strong>Solve for ( x )<\/strong>: Divide both sides by 99:<br>[<br>x = \\frac{12}{99}<br>]<\/li>\n\n\n\n<li><strong>Simplify the Fraction<\/strong>: We can simplify ( \\frac{12}{99} ) by finding the greatest common divisor (GCD) of 12 and 99, which is 3. Divide both the numerator and denominator by 3:<br>[<br>x = \\frac{12 \\div 3}{99 \\div 3} = \\frac{4}{33}<br>]<\/li>\n\n\n\n<li><strong>Final Answer<\/strong>: Thus, ( 0.12\\overline{12} ) can be expressed as the fraction ( \\frac{4}{33} ).<\/li>\n<\/ol>\n\n\n\n<p>In summary, the process involves defining the repeating decimal, multiplying to eliminate the repetition, forming a solvable equation, and then simplifying the result. The final simplified fraction representing ( 0.12\\overline{12} ) is ( \\frac{4}{33} ). This method can be applied to any repeating decimal to convert it into a fraction, making it a useful technique in mathematics.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is 0.12 repeating expressed as a fraction in simplest form The Correct Answer and Explanation is : The correct answer is: ( \\frac{4}{33} ) To express the repeating decimal ( 0.12\\overline{12} ) as a fraction, we can follow a systematic approach using algebra. In summary, the process involves defining the repeating decimal, multiplying to [&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-152484","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/152484","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=152484"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/152484\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=152484"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=152484"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=152484"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}