2.3 repeating as a fraction or percentage\u200b<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To express (2.3) repeating (denoted as (2.3\\overline{3})) as a fraction, follow these steps:<\/p>\n\n\n\n Let (x = 2.3\\overline{3}).<\/p>\n\n\n\n Since the repeating digit is “3,” multiply both sides of the equation by (10) to shift the decimal point:<\/p>\n\n\n\n [ Now, subtract the original (x) from this new equation:<\/p>\n\n\n\n [ This simplifies to:<\/p>\n\n\n\n [ To find (x), divide both sides by (9):<\/p>\n\n\n\n [ Now, simplify (\\frac{21}{9}):<\/p>\n\n\n\n [ So, (2.3\\overline{3} = \\frac{7}{3}) as a fraction.<\/p>\n\n\n\n To convert the fraction to a percentage, divide (7) by (3):<\/p>\n\n\n\n [ Now, to express it as a percentage, multiply by (100):<\/p>\n\n\n\n [ Thus, the repeating decimal (2.3\\overline{3}) can be expressed as the fraction (\\frac{7}{3}) and is approximately (233.33\\%) when converted to a percentage.<\/p>\n\n\n\n This process illustrates the connection between repeating decimals, fractions, and percentages, highlighting the importance of understanding the relationships between different numerical representations. It demonstrates that many decimals, especially repeating ones, can be expressed precisely as fractions, which can then be further translated into percentage form for easier interpretation in real-world applications, such as finance, statistics, and everyday calculations.<\/p>\n","protected":false},"excerpt":{"rendered":" 2.3 repeating as a fraction or percentage\u200b The Correct Answer and Explanation is : To express (2.3) repeating (denoted as (2.3\\overline{3})) as a fraction, follow these steps: Step 1: Set up the equation Let (x = 2.3\\overline{3}). Step 2: Multiply to eliminate the repeating part Since the repeating digit is “3,” multiply both sides of […]<\/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-147300","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/147300","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=147300"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/147300\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=147300"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=147300"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=147300"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Set up the equation<\/h3>\n\n\n\n
Step 2: Multiply to eliminate the repeating part<\/h3>\n\n\n\n
10x = 23.3\\overline{3}
]<\/p>\n\n\n\nStep 3: Set up another equation<\/h3>\n\n\n\n
10x – x = 23.3\\overline{3} – 2.3\\overline{3}
]<\/p>\n\n\n\n
9x = 21
]<\/p>\n\n\n\nStep 4: Solve for (x)<\/h3>\n\n\n\n
x = \\frac{21}{9}
]<\/p>\n\n\n\nStep 5: Simplify the fraction<\/h3>\n\n\n\n
x = \\frac{7}{3}
]<\/p>\n\n\n\nConverting to Percentage<\/h3>\n\n\n\n
7 \\div 3 \\approx 2.3333
]<\/p>\n\n\n\n
2.3333 \\times 100 \\approx 233.33\\%
]<\/p>\n\n\n\nSummary<\/h3>\n\n\n\n