What is 0.66666666666 as a fraction<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The correct answer is: (\\frac{2}{3})<\/strong><\/mark><\/p>\n\n\n\n The decimal number (0.66666666666) can be expressed as the fraction (\\frac{2}{3}). Here\u2019s how we can derive that:<\/p>\n\n\n\n The number (0.66666666666) is a repeating decimal, often written as (0.\\overline{6}). This notation indicates that the digit 6 repeats indefinitely.<\/p>\n\n\n\n Let\u2019s represent (x) as the repeating decimal: To eliminate the repeating part, multiply both sides of the equation by 10: Now we have two equations:<\/p>\n\n\n\n Next, subtract the first equation from the second: Now, divide both sides by 9: The fraction (\\frac{6}{9}) can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3: Thus, the decimal (0.66666666666) as a fraction is (\\frac{2}{3}). Understanding how to convert repeating decimals into fractions can be useful in various mathematical applications, including calculations, approximations, and number theory. This method illustrates a systematic approach to handling infinite decimal expansions.<\/p>\n","protected":false},"excerpt":{"rendered":" What is 0.66666666666 as a fraction The Correct Answer and Explanation is : The correct answer is: (\\frac{2}{3}) The decimal number (0.66666666666) can be expressed as the fraction (\\frac{2}{3}). Here\u2019s how we can derive that: Step 1: Understanding the Decimal The number (0.66666666666) is a repeating decimal, often written as (0.\\overline{6}). This notation indicates that […]<\/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-156332","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/156332","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=156332"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/156332\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=156332"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=156332"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=156332"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Understanding the Decimal<\/h3>\n\n\n\n
Step 2: Setting Up an Equation<\/h3>\n\n\n\n
[
x = 0.66666666666\\ldots
]<\/p>\n\n\n\nStep 3: Manipulating the Equation<\/h3>\n\n\n\n
[
10x = 6.66666666666\\ldots
]<\/p>\n\n\n\n\n
Step 4: Subtracting the Equations<\/h3>\n\n\n\n
[
10x – x = 6.66666666666\\ldots – 0.66666666666\\ldots
]
This simplifies to:
[
9x = 6
]<\/p>\n\n\n\nStep 5: Solving for (x)<\/h3>\n\n\n\n
[
x = \\frac{6}{9}
]<\/p>\n\n\n\nStep 6: Simplifying the Fraction<\/h3>\n\n\n\n
[
x = \\frac{6 \\div 3}{9 \\div 3} = \\frac{2}{3}
]<\/p>\n\n\n\nConclusion<\/h3>\n\n\n\n