Which simplified fraction is equal to 0.17 repeating<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To express the repeating decimal (0.17\\overline{17}) (which means that the digits “17” repeat indefinitely) as a simplified fraction, we can use algebraic methods.<\/p>\n\n\n\n Thus, the simplified fraction equivalent to the repeating decimal (0.17\\overline{17}) is: This fraction represents the same value as the original repeating decimal, and through the algebraic method outlined above, we\u2019ve successfully converted it into a simplified fraction. Repeating decimals can often be transformed into fractions using this method, which is particularly useful for understanding their precise values.<\/p>\n","protected":false},"excerpt":{"rendered":" Which simplified fraction is equal to 0.17 repeating The Correct Answer and Explanation is : To express the repeating decimal (0.17\\overline{17}) (which means that the digits “17” repeat indefinitely) as a simplified fraction, we can use algebraic methods. Step-by-Step Explanation Conclusion Thus, the simplified fraction equivalent to the repeating decimal (0.17\\overline{17}) is:[\\frac{17}{99}] This fraction represents […]<\/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-146185","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/146185","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=146185"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/146185\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=146185"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=146185"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=146185"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step-by-Step Explanation<\/h3>\n\n\n\n
\n
Let ( x = 0.171717\u2026)<\/li>\n\n\n\n
Since the repeating part has two digits, we can multiply both sides of the equation by 100 to shift the decimal point two places to the right:
[
100x = 17.171717\u2026
]<\/li>\n\n\n\n
Now, we have two equations:<\/li>\n<\/ol>\n\n\n\n\n
[
100x – x = 17.171717\u2026 – 0.171717\u2026
]
Simplifying both sides gives:
[
99x = 17
]<\/li>\n<\/ul>\n\n\n\n\n
To isolate (x), divide both sides by 99:
[
x = \\frac{17}{99}
]<\/li>\n\n\n\n
Next, we need to check if the fraction (\\frac{17}{99}) can be simplified. The numerator (17) is a prime number, and (99) can be factored into (3^2 \\times 11). Since (17) does not share any common factors with (99), the fraction is already in its simplest form.<\/li>\n<\/ol>\n\n\n\nConclusion<\/h3>\n\n\n\n
[
\\frac{17}{99}
]<\/p>\n\n\n\n