What’s 0.45 recurring 5 as a fraction in its simplest form? a) 9\/20 b) 4\/9 c) 5\/11 d) 1\/2<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To convert (0.45\\overline{5}) (0.455555\u2026) into a fraction, follow these steps:<\/p>\n\n\n\n Let (x) be equal to the repeating decimal:<\/p>\n\n\n\n [ Since the repeating part (5) starts after one digit, multiply both sides of the equation by 10:<\/p>\n\n\n\n [ Now, subtract the original equation (Step 1) from this new equation:<\/p>\n\n\n\n [ This simplifies to:<\/p>\n\n\n\n [ Now, express (4.1) as a fraction:<\/p>\n\n\n\n [ So the equation becomes:<\/p>\n\n\n\n [ Now solve for (x) by dividing both sides by 9:<\/p>\n\n\n\n [ The fraction (\\frac{41}{90}) is already in its simplest form because 41 is a prime number and does not share any common factors with 90.<\/p>\n\n\n\n Thus, the fraction form of (0.45\\overline{5}) is:<\/p>\n\n\n\n [ None of the given options (a) 9\/20, (b) 4\/9, (c) 5\/11, or (d) 1\/2 matches the correct answer (\\frac{41}{90}), so none of the choices are correct.<\/p>\n","protected":false},"excerpt":{"rendered":" What’s 0.45 recurring 5 as a fraction in its simplest form? a) 9\/20 b) 4\/9 c) 5\/11 d) 1\/2 The Correct Answer and Explanation is : To convert (0.45\\overline{5}) (0.455555\u2026) into a fraction, follow these steps: Step 1: Let (x = 0.45\\overline{5}) Let (x) be equal to the repeating decimal: [x = 0.4555555\\ldots] Step 2: […]<\/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-146230","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/146230","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=146230"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/146230\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=146230"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=146230"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=146230"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Let (x = 0.45\\overline{5})<\/h3>\n\n\n\n
x = 0.4555555\\ldots
]<\/p>\n\n\n\nStep 2: Multiply by 10 to shift the decimal<\/h3>\n\n\n\n
10x = 4.555555\\ldots
]<\/p>\n\n\n\n
10x – x = (4.555555\\ldots) – (0.455555\\ldots)
]<\/p>\n\n\n\n
9x = 4.1
]<\/p>\n\n\n\nStep 3: Solve for (x)<\/h3>\n\n\n\n
4.1 = \\frac{41}{10}
]<\/p>\n\n\n\n
9x = \\frac{41}{10}
]<\/p>\n\n\n\n
x = \\frac{41}{10 \\times 9} = \\frac{41}{90}
]<\/p>\n\n\n\nStep 4: Simplify the fraction<\/h3>\n\n\n\n
\\boxed{\\frac{41}{90}}
]<\/p>\n\n\n\nStep 5: Verify the answer choices<\/h3>\n\n\n\n