Express the repeating decimal as the ratio of two integers. 0.3 = 0.3333\u2026 The ratio of two integers 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 ( 0.3333\\ldots ) (also written as ( 0.\\overline{3} )) as a ratio of two integers, we need to convert the decimal into a fraction.<\/p>\n\n\n\n Thus, the repeating decimal ( 0.3333\\ldots ) is equivalent to the fraction ( \\frac{1}{3} ).<\/p>\n\n\n\n A repeating decimal occurs when a digit or group of digits repeats infinitely. In the case of ( 0.\\overline{3} ), the digit 3 repeats indefinitely. By using algebraic manipulation, we can convert repeating decimals into fractions, which can be expressed as the ratio of two integers. This is a common technique used in mathematics to simplify and work with repeating decimals. In this case, the repeating decimal ( 0.\\overline{3} ) simplifies to the fraction ( \\frac{1}{3} ), which is the ratio of the integers 1 and 3.<\/p>\n","protected":false},"excerpt":{"rendered":" Express the repeating decimal as the ratio of two integers. 0.3 = 0.3333\u2026 The ratio of two integers is . (Type an integer or a simplified fraction.) The Correct Answer and Explanation is : To express the repeating decimal ( 0.3333\\ldots ) (also written as ( 0.\\overline{3} )) as a ratio of two integers, we […]<\/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-189857","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/189857","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=189857"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/189857\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=189857"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=189857"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=189857"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step-by-step conversion process:<\/h3>\n\n\n\n
\n
Let ( x = 0.3333\\ldots ), where the digit 3 repeats infinitely.<\/li>\n\n\n\n
To get rid of the repeating decimal, multiply both sides of the equation by 10. This gives us:
[
10x = 3.3333\\ldots
]
Now, the decimal part on the right-hand side is the same as the original ( x ), so we can write the equation as:
[
10x = 3 + 0.3333\\ldots
]
Therefore, we have:
[
10x = 3 + x
]<\/li>\n\n\n\n
Now, subtract ( x ) from both sides to isolate ( x ) on one side of the equation:
[
10x – x = 3
]
Simplifying this:
[
9x = 3
]
Finally, solve for ( x ) by dividing both sides by 9:
[
x = \\frac{3}{9}
]<\/li>\n\n\n\n
The fraction ( \\frac{3}{9} ) can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 3:
[
x = \\frac{3 \\div 3}{9 \\div 3} = \\frac{1}{3}
]<\/li>\n<\/ol>\n\n\n\nFinal result:<\/h3>\n\n\n\n
Explanation:<\/h3>\n\n\n\n