What is the recurring decimal 0.1 as a fraction in its simplest form?<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To express the recurring decimal ( 0.1 ) (specifically, ( 0.111\u2026) where the digit “1” repeats indefinitely) as a fraction, we can follow a systematic approach.<\/p>\n\n\n\n Let\u2019s denote the recurring decimal as ( x ): To eliminate the decimal, we can multiply both sides of the equation by ( 10 ): Now, we have two equations:<\/p>\n\n\n\n Next, we can subtract the first equation from the second: To isolate ( x ), we divide both sides by ( 9 ): Thus, the recurring decimal ( 0.111\u2026) can be expressed as the fraction ( \\frac{1}{9} ).<\/p>\n\n\n\n To verify that this fraction is in its simplest form, we need to check for any common factors between the numerator and the denominator. The number ( 1 ) is a prime number and only has factors of ( 1 ) and ( 1 ). The number ( 9 ) factors into ( 3 \\times 3 ). Since ( 1 ) and ( 9 ) share no common factors other than ( 1 ), ( \\frac{1}{9} ) is indeed in its simplest form.<\/p>\n\n\n\n In conclusion, the recurring decimal ( 0.111\u2026) can be expressed as the fraction ( \\frac{1}{9} ). This process illustrates how to convert a repeating decimal into a fraction by using algebraic manipulation, making it clear and straightforward to find the simplest form of the fraction.<\/p>\n","protected":false},"excerpt":{"rendered":" What is the recurring decimal 0.1 as a fraction in its simplest form? The Correct Answer and Explanation is : To express the recurring decimal ( 0.1 ) (specifically, ( 0.111\u2026) where the digit “1” repeats indefinitely) as a fraction, we can follow a systematic approach. Let\u2019s denote the recurring decimal as ( x ):[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-157171","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/157171","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=157171"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/157171\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=157171"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=157171"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=157171"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
[
x = 0.111\u2026\\text{ (where the digit “1” repeats)}
]<\/p>\n\n\n\n
[
10x = 1.111\u2026\\text{ (the “1” still repeats)}
]<\/p>\n\n\n\n\n
[
10x – x = 1.111\u2026 – 0.111\u2026
]
This simplifies to:
[
9x = 1
]<\/p>\n\n\n\n
[
x = \\frac{1}{9}
]<\/p>\n\n\n\n