What is 0.36 repeating expressed as a fraction in simplest form?<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To express ( 0.\\overline{36} ) (which means 0.363636\u2026, where “36” repeats indefinitely) as a fraction, follow these steps:<\/p>\n\n\n\n We will set up an equation where ( x ) represents the repeating decimal: To eliminate the repeating part, multiply both sides of the equation by 100 (since “36” consists of two digits, multiplying by 100 shifts the decimal point two places to the right): Now, subtract the original equation ( x = 0.\\overline{36} ) from the equation ( 100x = 36.\\overline{36} ): To solve for ( x ), divide both sides by 99: To simplify ( \\frac{36}{99} ), find the greatest common divisor (GCD) of 36 and 99. The GCD of 36 and 99 is 9. Now, divide both the numerator and the denominator by 9: Thus, ( 0.\\overline{36} = \\frac{4}{11} ).<\/p>\n\n\n\n The repeating decimal ( 0.\\overline{36} ) is equivalent to the fraction ( \\frac{4}{11} ).<\/p>\n\n\n\n This process works because by subtracting the equation where the repeating decimal is shifted, we can eliminate the repeating part. The result is a simple fraction, and simplifying that fraction makes it easier to work with and understand. This method of converting repeating decimals into fractions is a standard technique in algebra.<\/p>\n","protected":false},"excerpt":{"rendered":" What is 0.36 repeating expressed as a fraction in simplest form? The Correct Answer and Explanation is : To express ( 0.\\overline{36} ) (which means 0.363636\u2026, where “36” repeats indefinitely) as a fraction, follow these steps: Step 1: Let ( x = 0.\\overline{36} ) We will set up an equation where ( x ) represents […]<\/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-163172","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/163172","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=163172"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/163172\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=163172"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=163172"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=163172"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Let ( x = 0.\\overline{36} )<\/h3>\n\n\n\n
[
x = 0.\\overline{36}
]<\/p>\n\n\n\nStep 2: Eliminate the repeating decimal<\/h3>\n\n\n\n
[
100x = 36.\\overline{36}
]<\/p>\n\n\n\nStep 3: Subtract the original equation from the new equation<\/h3>\n\n\n\n
[
100x – x = 36.\\overline{36} – 0.\\overline{36}
]
Simplifying both sides:
[
99x = 36
]<\/p>\n\n\n\nStep 4: Solve for ( x )<\/h3>\n\n\n\n
[
x = \\frac{36}{99}
]<\/p>\n\n\n\nStep 5: Simplify the fraction<\/h3>\n\n\n\n
[
\\frac{36}{99} = \\frac{36 \\div 9}{99 \\div 9} = \\frac{4}{11}
]<\/p>\n\n\n\nConclusion<\/h3>\n\n\n\n
Explanation<\/h3>\n\n\n\n