{"id":151495,"date":"2024-10-10T06:52:24","date_gmt":"2024-10-10T06:52:24","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=151495"},"modified":"2024-10-10T06:52:27","modified_gmt":"2024-10-10T06:52:27","slug":"write-the-fraction-for-the-recurring-decimal","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/10\/write-the-fraction-for-the-recurring-decimal\/","title":{"rendered":"Write the fraction for the recurring decimal"},"content":{"rendered":"\n<p>Write the fraction for the recurring decimal\u2026 a 0.77777<\/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{7}{9} )<\/strong><\/mark><\/p>\n\n\n\n<p>To convert the recurring decimal ( 0.77777\\ldots ) (where the 7s repeat indefinitely) into a fraction, we can follow a systematic approach.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Set Up an Equation<\/h3>\n\n\n\n<p>Let ( x = 0.77777\\ldots ).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Eliminate the Recurring Part<\/h3>\n\n\n\n<p>To isolate the repeating part, we can multiply both sides of the equation by 10. This will shift the decimal point one place to the right:<\/p>\n\n\n\n<p>[<br>10x = 7.77777\\ldots<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Subtract the Original Equation<\/h3>\n\n\n\n<p>Now, we have two equations:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>( x = 0.77777\\ldots ) (1)<\/li>\n\n\n\n<li>( 10x = 7.77777\\ldots ) (2)<\/li>\n<\/ol>\n\n\n\n<p>Next, subtract equation (1) from equation (2):<\/p>\n\n\n\n<p>[<br>10x &#8211; x = 7.77777\\ldots &#8211; 0.77777\\ldots<br>]<\/p>\n\n\n\n<p>This simplifies to:<\/p>\n\n\n\n<p>[<br>9x = 7<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Solve for ( x )<\/h3>\n\n\n\n<p>Now, we can solve for ( x ):<\/p>\n\n\n\n<p>[<br>x = \\frac{7}{9}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>Thus, the fraction representation of the recurring decimal ( 0.77777\\ldots ) is ( \\frac{7}{9} ).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Verification<\/h3>\n\n\n\n<p>To verify that ( \\frac{7}{9} ) is indeed equal to ( 0.77777\\ldots ), we can perform the division ( 7 \\div 9 ):<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>9 goes into 7 zero times. We write down a zero and a decimal point, and bring down a zero, making it 70.<\/li>\n\n\n\n<li>9 goes into 70 seven times (since ( 9 \\times 7 = 63 )).<\/li>\n\n\n\n<li>Subtracting gives us a remainder of 7.<\/li>\n\n\n\n<li>Bringing down another zero gives us 70 again, repeating the process.<\/li>\n<\/ul>\n\n\n\n<p>This cycle will continue indefinitely, confirming that ( \\frac{7}{9} = 0.77777\\ldots ).<\/p>\n\n\n\n<p>In summary, the recurring decimal ( 0.77777\\ldots ) can be expressed as the fraction ( \\frac{7}{9} ), and through algebraic manipulation and verification, we see that this conversion is accurate.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Write the fraction for the recurring decimal\u2026 a 0.77777 The Correct Answer and Explanation is : The correct answer is: ( \\frac{7}{9} ) To convert the recurring decimal ( 0.77777\\ldots ) (where the 7s repeat indefinitely) into a fraction, we can follow a systematic approach. Step 1: Set Up an Equation Let ( x = [&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-151495","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/151495","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=151495"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/151495\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=151495"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=151495"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=151495"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}