1.66666666667 as a fraction in simplest form<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n The decimal ( 1.66666666667 ) is a repeating decimal, often written as ( 1.\\overline{6} ), where the 6 repeats indefinitely. To convert this repeating decimal into a fraction in its simplest form, we need to follow a series of steps.<\/p>\n\n\n\n Let ( x = 1.\\overline{6} ), meaning that ( x ) represents the repeating decimal.<\/p>\n\n\n\n To eliminate the repeating part, multiply both sides of the equation by 10. This shifts the decimal point one place to the right: Next, subtract the first equation from the second: Now, solve for ( x ) by dividing both sides of the equation by 9: The fraction ( \\frac{15}{9} ) can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 3: Thus, the decimal ( 1.\\overline{6} ) (or ( 1.66666666667 )) as a fraction in simplest form is ( \\frac{5}{3} ).<\/p>\n\n\n\n The decimal ( 1.\\overline{6} ) is equivalent to the fraction ( \\frac{5}{3} ). This process demonstrates how to convert repeating decimals to fractions by isolating the repeating part, subtracting equations, and simplifying the result.<\/p>\n","protected":false},"excerpt":{"rendered":" 1.66666666667 as a fraction in simplest form The Correct Answer and Explanation is: The decimal ( 1.66666666667 ) is a repeating decimal, often written as ( 1.\\overline{6} ), where the 6 repeats indefinitely. To convert this repeating decimal into a fraction in its simplest form, we need to follow a series of steps. Step 1: […]<\/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-168576","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168576","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=168576"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168576\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=168576"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=168576"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=168576"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Set the decimal equal to a variable<\/h3>\n\n\n\n
Step 2: Eliminate the repeating part<\/h3>\n\n\n\n
[
10x = 16.\\overline{6}
]
Now we have two equations:<\/p>\n\n\n\n\n
Step 3: Subtract the equations<\/h3>\n\n\n\n
[
10x – x = 16.\\overline{6} – 1.\\overline{6}
]
This simplifies to:
[
9x = 15
]
The repeating decimals cancel out.<\/p>\n\n\n\nStep 4: Solve for ( x )<\/h3>\n\n\n\n
[
x = \\frac{15}{9}
]<\/p>\n\n\n\nStep 5: Simplify the fraction<\/h3>\n\n\n\n
[
x = \\frac{15 \\div 3}{9 \\div 3} = \\frac{5}{3}
]<\/p>\n\n\n\nConclusion<\/h3>\n\n\n\n