0.75 repeating 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{75} ) (which is 0.757575\u2026) as a fraction in simplest form, we can use a method that involves algebraic manipulation.<\/p>\n\n\n\n Let ( x ) represent the repeating decimal, so: Multiply both sides of the equation by 100 to shift the decimal point two places to the right: Now, we have two equations:<\/p>\n\n\n\n Subtract the first equation from the second: Now, solve for ( x ) by dividing both sides of the equation by 99: Next, simplify the fraction ( \\frac{75}{99} ). The greatest common divisor (GCD) of 75 and 99 is 3. To simplify, divide both the numerator and denominator by 3: Thus, ( 0.\\overline{75} ) as a fraction is ( \\frac{25}{33} ).<\/p>\n\n\n\n The repeating decimal ( 0.\\overline{75} ) is equivalent to the fraction ( \\frac{25}{33} ) in its simplest form.<\/p>\n\n\n\n This method of converting repeating decimals to fractions is based on algebraic manipulation and shows how to deal with repeating patterns by eliminating them step by step.<\/p>\n","protected":false},"excerpt":{"rendered":" 0.75 repeating as a fraction in simplest form The Correct Answer and Explanation is : To express ( 0.\\overline{75} ) (which is 0.757575\u2026) as a fraction in simplest form, we can use a method that involves algebraic manipulation. Step 1: Let ( x = 0.\\overline{75} ). Let ( x ) represent the repeating decimal, so:[x […]<\/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-164117","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/164117","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=164117"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/164117\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=164117"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=164117"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=164117"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Let ( x = 0.\\overline{75} ).<\/h3>\n\n\n\n
[
x = 0.75757575\\ldots
]<\/p>\n\n\n\nStep 2: Eliminate the repeating part.<\/h3>\n\n\n\n
[
100x = 75.757575\\ldots
]<\/p>\n\n\n\n\n
Step 3: Subtract the two equations.<\/h3>\n\n\n\n
[
100x – x = 75.757575\\ldots – 0.757575\\ldots
]
This simplifies to:
[
99x = 75
]<\/p>\n\n\n\nStep 4: Solve for ( x ).<\/h3>\n\n\n\n
[
x = \\frac{75}{99}
]<\/p>\n\n\n\nStep 5: Simplify the fraction.<\/h3>\n\n\n\n
[
\\frac{75}{99} = \\frac{75 \\div 3}{99 \\div 3} = \\frac{25}{33}
]<\/p>\n\n\n\nConclusion:<\/h3>\n\n\n\n