Express the repeating decimal as the ratio of two integers. 0.03 = 0.0333\u2026 1. The ratio that represents the repeating decimal is (Type an integer or a simplified fraction.)<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To express the repeating decimal ( 0.0333\\ldots ) (where the 3 repeats indefinitely) as a ratio of two integers, we need to convert the repeating decimal into a fraction.<\/p>\n\n\n\n Thus, the repeating decimal ( 0.0333\\ldots ) is equal to the fraction ( \\frac{1}{30} ).<\/p>\n\n\n\n The repeating decimal ( 0.0333\\ldots ) (where the 3 repeats indefinitely) can be expressed as the ratio ( \\frac{1}{30} ). This conversion shows how repeating decimals can be transformed into simple fractions using algebraic methods, which is useful for many applications in mathematics.<\/p>\n","protected":false},"excerpt":{"rendered":" Express the repeating decimal as the ratio of two integers. 0.03 = 0.0333\u2026 1. The ratio that represents the repeating decimal is (Type an integer or a simplified fraction.) The Correct Answer and Explanation is : To express the repeating decimal ( 0.0333\\ldots ) (where the 3 repeats indefinitely) as a ratio of two integers, […]<\/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-189855","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/189855","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=189855"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/189855\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=189855"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=189855"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=189855"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step-by-step process:<\/h3>\n\n\n\n
\n
[
10x = 0.3333\\ldots
]<\/li>\n\n\n\n
[
10x – x = 0.3333\\ldots – 0.0333\\ldots
]
Simplifying this:
[
9x = 0.3
]<\/li>\n\n\n\n
[
x = \\frac{0.3}{9}
]<\/li>\n\n\n\n
[
0.3 = \\frac{3}{10}
]
So now the equation becomes:
[
x = \\frac{\\frac{3}{10}}{9}
]<\/li>\n\n\n\n
[
x = \\frac{3}{10} \\times \\frac{1}{9} = \\frac{3}{90}
]<\/li>\n\n\n\n
[
\\frac{3}{90} = \\frac{1}{30}
]<\/li>\n<\/ol>\n\n\n\nConclusion:<\/h3>\n\n\n\n