Write 2.5 repeating as a mixed number in simplest form.<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To convert the decimal (2.5) (which is (2.5) repeating) into a mixed number, we first represent it mathematically. The decimal (2.5) repeating can be expressed as (2.\\overline{5}), where the digit (5) repeats indefinitely.<\/p>\n\n\n\n Let (x = 2.\\overline{5}). This means that:<\/p>\n\n\n\n [ To eliminate the repeating part, we can multiply (x) by (10) (since the repeating digit is in the tenths place):<\/p>\n\n\n\n [ Now, we have two equations:<\/p>\n\n\n\n Now we subtract the first equation from the second:<\/p>\n\n\n\n [ This simplifies to:<\/p>\n\n\n\n [ Next, divide both sides by (9):<\/p>\n\n\n\n [ To convert the improper fraction (\\frac{23}{9}) into a mixed number, we perform the division:<\/p>\n\n\n\n Thus, we can express (\\frac{23}{9}) as:<\/p>\n\n\n\n [ Therefore, the mixed number form of (2.5) repeating (or (2.\\overline{5})) is:<\/p>\n\n\n\n [ This mixed number is in simplest form because (5) and (9) have no common factors other than (1).<\/p>\n","protected":false},"excerpt":{"rendered":" Write 2.5 repeating as a mixed number in simplest form. The Correct Answer and Explanation is : To convert the decimal (2.5) (which is (2.5) repeating) into a mixed number, we first represent it mathematically. The decimal (2.5) repeating can be expressed as (2.\\overline{5}), where the digit (5) repeats indefinitely. Step 1: Setting Up the […]<\/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-143427","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/143427","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=143427"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/143427\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=143427"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=143427"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=143427"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Setting Up the Equation<\/h3>\n\n\n\n
x = 2.55555\\ldots
]<\/p>\n\n\n\nStep 2: Eliminating the Repeating Decimal<\/h3>\n\n\n\n
10x = 25.55555\\ldots
]<\/p>\n\n\n\n\n
Step 3: Subtracting the Two Equations<\/h3>\n\n\n\n
10x – x = 25.55555\\ldots – 2.55555\\ldots
]<\/p>\n\n\n\n
9x = 23
]<\/p>\n\n\n\nStep 4: Solving for (x)<\/h3>\n\n\n\n
x = \\frac{23}{9}
]<\/p>\n\n\n\nStep 5: Converting to Mixed Number<\/h3>\n\n\n\n
\n
2 \\frac{5}{9}
]<\/p>\n\n\n\nConclusion<\/h3>\n\n\n\n
2 \\frac{5}{9}
]<\/p>\n\n\n\n