What is 0.16666666666 as a fraction?<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The decimal number (0.16666666666) can be expressed as a fraction. This decimal is a repeating decimal, specifically (0.1\\overline{6}), which means it has a repeating pattern of 6 after the decimal point. To convert it to a fraction, we can follow a systematic approach.<\/p>\n\n\n\n Let (x = 0.1\\overline{6}).<\/p>\n\n\n\n To eliminate the repeating decimal, we can multiply (x) by 10 to shift the decimal point:<\/p>\n\n\n\n [ Now we have two equations:<\/p>\n\n\n\n Subtract the first equation from the second:<\/p>\n\n\n\n [ Now, we solve for (x):<\/p>\n\n\n\n [ We can simplify (\\frac{1.5}{9}). To make it easier, we can express (1.5) as (\\frac{15}{10}):<\/p>\n\n\n\n [ Now we can simplify (\\frac{15}{90}) by dividing both the numerator and denominator by 15:<\/p>\n\n\n\n [ Thus, the decimal (0.16666666666) is equivalent to the fraction (\\frac{1}{6}). This method illustrates the process of converting a repeating decimal into a fraction, demonstrating the utility of algebraic manipulation to solve problems involving decimal representations. The result shows that fractions can provide a precise representation of decimal values, particularly when dealing with repeating patterns.<\/p>\n","protected":false},"excerpt":{"rendered":" What is 0.16666666666 as a fraction? The Correct Answer and Explanation is : The decimal number (0.16666666666) can be expressed as a fraction. This decimal is a repeating decimal, specifically (0.1\\overline{6}), which means it has a repeating pattern of 6 after the decimal point. To convert it to a fraction, we can follow a systematic […]<\/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-145569","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/145569","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=145569"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/145569\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=145569"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=145569"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=145569"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Define the Decimal<\/h3>\n\n\n\n
Step 2: Eliminate the Repeating Part<\/h3>\n\n\n\n
10x = 1.66666666666\\ldots
]<\/p>\n\n\n\nStep 3: Set Up an Equation<\/h3>\n\n\n\n
\n
Step 4: Subtract the First Equation from the Second<\/h3>\n\n\n\n
10x – x = 1.66666666666\\ldots – 0.16666666666\\ldots
]
[
9x = 1.5
]<\/p>\n\n\n\nStep 5: Solve for (x)<\/h3>\n\n\n\n
x = \\frac{1.5}{9}
]<\/p>\n\n\n\nStep 6: Simplify the Fraction<\/h3>\n\n\n\n
x = \\frac{15}{10 \\times 9} = \\frac{15}{90}
]<\/p>\n\n\n\n
x = \\frac{1}{6}
]<\/p>\n\n\n\nConclusion<\/h3>\n\n\n\n