2.6 repeated simplified as a fraction Please help asap!!!<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To convert the repeating decimal ( 2.6\\overline{6} ) (which means ( 2.66666\u2026 )) into a fraction, we can use a method involving algebra.<\/p>\n\n\n\n Let ( x = 2.6\\overline{6} ). This gives us the equation:<\/p>\n\n\n\n [ To isolate the repeating part, multiply both sides of the equation by 10. This shifts the decimal point one place to the right:<\/p>\n\n\n\n [ Now, we have two equations:<\/p>\n\n\n\n Next, subtract the first equation from the second to eliminate the repeating part:<\/p>\n\n\n\n [ This simplifies to:<\/p>\n\n\n\n [ Now, divide both sides by 9:<\/p>\n\n\n\n [ To simplify ( \\frac{24}{9} ), find the greatest common divisor (GCD) of 24 and 9. The GCD is 3. Now divide both the numerator and denominator by 3:<\/p>\n\n\n\n [ Thus, the repeating decimal ( 2.6\\overline{6} ) can be expressed as the fraction ( \\frac{8}{3} ). This method of converting repeating decimals to fractions can be applied to other repeating decimals as well by using a similar algebraic approach.<\/p>\n","protected":false},"excerpt":{"rendered":" 2.6 repeated simplified as a fraction Please help asap!!! The Correct Answer and Explanation is : To convert the repeating decimal ( 2.6\\overline{6} ) (which means ( 2.66666\u2026 )) into a fraction, we can use a method involving algebra. Step 1: Set Up the Equation Let ( x = 2.6\\overline{6} ). This gives us the […]<\/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-146587","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/146587","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=146587"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/146587\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=146587"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=146587"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=146587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Set Up the Equation<\/h3>\n\n\n\n
x = 2.66666\\ldots
]<\/p>\n\n\n\nStep 2: Eliminate the Repeating Part<\/h3>\n\n\n\n
10x = 26.66666\\ldots
]<\/p>\n\n\n\nStep 3: Set Up Another Equation<\/h3>\n\n\n\n
\n
Step 4: Subtract the Two Equations<\/h3>\n\n\n\n
10x – x = 26.66666\\ldots – 2.66666\\ldots
]<\/p>\n\n\n\n
9x = 24
]<\/p>\n\n\n\nStep 5: Solve for ( x )<\/h3>\n\n\n\n
x = \\frac{24}{9}
]<\/p>\n\n\n\nStep 6: Simplify the Fraction<\/h3>\n\n\n\n
x = \\frac{24 \\div 3}{9 \\div 3} = \\frac{8}{3}
]<\/p>\n\n\n\nConclusion<\/h3>\n\n\n\n