Is 5.3 repeating rational<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n Yes, 5.3 repeating (denoted as ( 5.\\overline{3} )) is a rational number.<\/p>\n\n\n\n A rational number<\/strong> is defined as any number that can be expressed as the ratio of two integers. Specifically, if a number can be written in the form ( \\frac{a}{b} ), where ( a ) and ( b ) are integers and ( b \\neq 0 ), then the number is rational.<\/p>\n\n\n\n Now, let’s examine ( 5.\\overline{3} ), which means the digit 3 repeats indefinitely:<\/p>\n\n\n\n [ To show that this number is rational, we can convert it into a fraction. Here’s a step-by-step process:<\/p>\n\n\n\n Thus, ( 5.\\overline{3} = \\frac{16}{3} ), which is a rational number because it can be expressed as the ratio of two integers.<\/p>\n\n\n\n The key takeaway is that repeating decimals are always rational numbers. If a decimal repeats or terminates, it can be written as a fraction. This is in contrast to irrational numbers, which cannot be expressed as a fraction (e.g., ( \\pi ), ( \\sqrt{2} ), etc.), and have non-repeating, non-terminating decimals.<\/p>\n\n\n\n In conclusion, ( 5.\\overline{3} ) is a rational number because it can be expressed as ( \\frac{16}{3} ), which is a ratio of two integers.<\/p>\n","protected":false},"excerpt":{"rendered":" Is 5.3 repeating rational The Correct Answer and Explanation is : Yes, 5.3 repeating (denoted as ( 5.\\overline{3} )) is a rational number. Explanation: A rational number is defined as any number that can be expressed as the ratio of two integers. Specifically, if a number can be written in the form ( \\frac{a}{b} ), […]<\/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-163185","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/163185","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=163185"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/163185\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=163185"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=163185"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=163185"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Explanation:<\/h3>\n\n\n\n
5.\\overline{3} = 5.33333\\ldots
]<\/p>\n\n\n\n\n
[
10x = 53.\\overline{3}
]<\/li>\n\n\n\n
[
10x – x = 53.\\overline{3} – 5.\\overline{3}
]
This simplifies to:
[
9x = 48
]<\/li>\n\n\n\n
[
x = \\frac{48}{9}
]<\/li>\n\n\n\n
[
x = \\frac{16}{3}
]<\/li>\n<\/ol>\n\n\n\nWhy is this important?<\/h3>\n\n\n\n