Write 0.32 repeating as a fraction in simplest form.<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The correct answer is: {\\frac{97}{300}}<\/strong><\/mark><\/p>\n\n\n\n To convert the repeating decimal (0.32\\overline{3}) (which can be written as (0.323333\u2026)) into a fraction, we can follow a systematic approach.<\/p>\n\n\n\n Let (x = 0.323333\u2026).<\/p>\n\n\n\n To eliminate the repeating part, we can multiply (x) by 10 to move the decimal point one place to the right. This gives us:<\/p>\n\n\n\n [ Next, we want to align the repeating decimals. To do this, we can multiply (x) by 100, which moves the decimal point two places to the right:<\/p>\n\n\n\n [ Now we have two equations:<\/p>\n\n\n\n Next, we subtract equation 1 from equation 2:<\/p>\n\n\n\n [ This simplifies to:<\/p>\n\n\n\n [ Calculating the right side:<\/p>\n\n\n\n [ Thus, we have:<\/p>\n\n\n\n [ To find (x), divide both sides by 90:<\/p>\n\n\n\n [ To eliminate the decimal in the numerator, we can multiply the numerator and denominator by 10:<\/p>\n\n\n\n [ Now, we simplify (\\frac{291}{900}). The greatest common divisor (GCD) of 291 and 900 is 3. So we divide both the numerator and denominator by 3:<\/p>\n\n\n\n [ Thus, the fraction representation of the repeating decimal (0.32\\overline{3}) is:<\/p>\n\n\n\n [ This is the simplest form of the fraction.<\/p>\n","protected":false},"excerpt":{"rendered":" Write 0.32 repeating as a fraction in simplest form. The Correct Answer and Explanation is : The correct answer is: {\\frac{97}{300}} To convert the repeating decimal (0.32\\overline{3}) (which can be written as (0.323333\u2026)) into a fraction, we can follow a systematic approach. Step 1: Define the repeating decimal Let (x = 0.323333\u2026). Step 2: Isolate […]<\/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-150545","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/150545","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=150545"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/150545\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=150545"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=150545"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=150545"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Define the repeating decimal<\/h3>\n\n\n\n
Step 2: Isolate the repeating part<\/h3>\n\n\n\n
10x = 3.23333\u2026
]<\/p>\n\n\n\nStep 3: Align the repeating decimals<\/h3>\n\n\n\n
100x = 32.3333\u2026
]<\/p>\n\n\n\n\n
Step 4: Subtract the equations<\/h3>\n\n\n\n
100x – 10x = 32.3333\u2026 – 3.23333\u2026
]<\/p>\n\n\n\n
90x = 32.3333\u2026 – 3.23333\u2026
]<\/p>\n\n\n\n
32.3333\u2026 – 3.23333\u2026 = 29.1
]<\/p>\n\n\n\n
90x = 29.1
]<\/p>\n\n\n\nStep 5: Solve for (x)<\/h3>\n\n\n\n
x = \\frac{29.1}{90}
]<\/p>\n\n\n\nStep 6: Eliminate the decimal in the numerator<\/h3>\n\n\n\n
x = \\frac{291}{900}
]<\/p>\n\n\n\nStep 7: Simplify the fraction<\/h3>\n\n\n\n
x = \\frac{291 \\div 3}{900 \\div 3} = \\frac{97}{300}
]<\/p>\n\n\n\nFinal Result<\/h3>\n\n\n\n
\\boxed{\\frac{97}{300}}
]<\/p>\n\n\n\n