{"id":161529,"date":"2024-11-04T20:50:19","date_gmt":"2024-11-04T20:50:19","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=161529"},"modified":"2024-11-04T20:50:22","modified_gmt":"2024-11-04T20:50:22","slug":"what-is-0-48-repeating-as-a-fraction-in-simplest-form","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/04\/what-is-0-48-repeating-as-a-fraction-in-simplest-form\/","title":{"rendered":"What is 0.48 repeating as a fraction in simplest form"},"content":{"rendered":"\n<p>What is 0.48 repeating as a fraction in simplest form?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To convert the repeating decimal (0.48\\overline{48}) (where &#8220;48&#8221; repeats indefinitely) into a fraction, we can follow a systematic approach.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Let (x) be the repeating decimal.<\/h3>\n\n\n\n<p>Let:<br>[<br>x = 0.48484848\\ldots<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Multiply (x) by a power of 10 to shift the decimal point.<\/h3>\n\n\n\n<p>Since &#8220;48&#8221; has two digits, we multiply (x) by (100) to shift the decimal point two places to the right:<br>[<br>100x = 48.48484848\\ldots<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Set up an equation to eliminate the repeating part.<\/h3>\n\n\n\n<p>Now we have two equations:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>(x = 0.48484848\\ldots)<\/li>\n\n\n\n<li>(100x = 48.48484848\\ldots)<\/li>\n<\/ol>\n\n\n\n<p>Next, we subtract the first equation from the second to eliminate the repeating decimal:<br>[<br>100x &#8211; x = 48.48484848\\ldots &#8211; 0.48484848\\ldots<br>]<br>This simplifies to:<br>[<br>99x = 48<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Solve for (x).<\/h3>\n\n\n\n<p>Now, we solve for (x):<br>[<br>x = \\frac{48}{99}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 5: Simplify the fraction.<\/h3>\n\n\n\n<p>To simplify (\\frac{48}{99}), we need to find the greatest common divisor (GCD) of (48) and (99).<\/p>\n\n\n\n<p>The prime factorization of (48) is (2^4 \\times 3), and for (99) it is (3^2 \\times 11). The GCD is (3) since it&#8217;s the only common factor.<\/p>\n\n\n\n<p>Now, divide both the numerator and the denominator by their GCD:<br>[<br>\\frac{48 \\div 3}{99 \\div 3} = \\frac{16}{33}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>Thus, the repeating decimal (0.48\\overline{48}) can be expressed as the fraction (\\frac{16}{33}) in its simplest form. This fraction represents the same value as the repeating decimal, confirming that our conversion was accurate.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is 0.48 repeating as a fraction in simplest form? The Correct Answer and Explanation is: To convert the repeating decimal (0.48\\overline{48}) (where &#8220;48&#8221; repeats indefinitely) into a fraction, we can follow a systematic approach. Step 1: Let (x) be the repeating decimal. Let:[x = 0.48484848\\ldots] Step 2: Multiply (x) by a power of 10 [&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-161529","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/161529","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=161529"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/161529\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=161529"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=161529"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=161529"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}