What is the fractional form of 0.8 repeating<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To convert the repeating decimal ( 0.\\overline{8} ) (where the 8 repeats infinitely) into a fraction, we follow a systematic algebraic approach. Let’s go through the steps in detail:<\/p>\n\n\n\n Let ( x = 0.\\overline{8} ), which means:<\/p>\n\n\n\n [ Now, to eliminate the repeating decimal, we multiply both sides of the equation by 10, because the decimal repeats after one digit (the 8). This gives:<\/p>\n\n\n\n [ We now have two equations:<\/p>\n\n\n\n Subtract equation 1 from equation 2 to eliminate the repeating decimals:<\/p>\n\n\n\n [ This simplifies to:<\/p>\n\n\n\n [ Now, solve for ( x ) by dividing both sides of the equation by 9:<\/p>\n\n\n\n [ Thus, the fractional form of ( 0.\\overline{8} ) is ( \\frac{8}{9} ).<\/p>\n\n\n\n The reason why ( 0.\\overline{8} ) equals ( \\frac{8}{9} ) is that repeating decimals are often equivalent to fractions, which can be determined by the algebraic method shown above. This approach works for any repeating decimal, not just for 0.8 repeating. It’s important to note that some people might assume that ( 0.\\overline{8} ) is simply 1, because ( 0.\\overline{9} = 1 ). However, through the above algebraic steps, we see that ( 0.\\overline{8} ) is strictly equal to ( \\frac{8}{9} ), a value that is slightly less than 1 but very close to it.<\/p>\n","protected":false},"excerpt":{"rendered":" What is the fractional form of 0.8 repeating The Correct Answer and Explanation is: To convert the repeating decimal ( 0.\\overline{8} ) (where the 8 repeats infinitely) into a fraction, we follow a systematic algebraic approach. Let’s go through the steps in detail: Step 1: Represent the Repeating Decimal as a Variable Let ( 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-168320","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168320","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=168320"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168320\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=168320"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=168320"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=168320"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Represent the Repeating Decimal as a Variable<\/h3>\n\n\n\n
x = 0.88888\\ldots
]<\/p>\n\n\n\nStep 2: Eliminate the Repeating Part<\/h3>\n\n\n\n
10x = 8.88888\\ldots
]<\/p>\n\n\n\nStep 3: Set Up a System of Equations<\/h3>\n\n\n\n
\n
Step 4: Subtract the First Equation from the Second<\/h3>\n\n\n\n
(10x – x) = (8.88888\\ldots – 0.88888\\ldots)
]<\/p>\n\n\n\n
9x = 8
]<\/p>\n\n\n\nStep 5: Solve for ( x )<\/h3>\n\n\n\n
x = \\frac{8}{9}
]<\/p>\n\n\n\nFinal Answer:<\/h3>\n\n\n\n
Explanation:<\/h3>\n\n\n\n