Express the number as a ratio of integers. <\/p>\n\n\n\n
0.26 = 0.26262626 . ..<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To express the repeating decimal 0.26262626…0.26262626… as a ratio of integers, we can follow a systematic method.<\/p>\n\n\n\n Let x=0.26262626…x = 0.26262626…. Notice that the decimal repeats every two digits, “26”. We want to eliminate the repeating part by using algebraic manipulation.<\/p>\n\n\n\n Since the decimal repeats every two digits, we multiply both sides of the equation by 100 to shift the decimal point two places to the right: 100x=26.26262626…100x = 26.26262626…<\/p>\n\n\n\n Now, subtract the original equation x=0.26262626…x = 0.26262626… from the equation 100x=26.26262626…100x = 26.26262626…: 100x\u2212x=26.26262626…\u22120.26262626…100x – x = 26.26262626… – 0.26262626…<\/p>\n\n\n\n This simplifies to: 99x=2699x = 26<\/p>\n\n\n\n Now that we have 99x=2699x = 26, divide both sides by 99 to solve for xx: x=2699x = \\frac{26}{99}<\/p>\n\n\n\n Thus, 0.26262626…0.26262626… can be written as the fraction 2699\\frac{26}{99}.<\/p>\n\n\n\n To verify, divide 2626 by 9999: 2699\u22480.26262626…\\frac{26}{99} \\approx 0.26262626…<\/p>\n\n\n\n This confirms that the repeating decimal 0.26262626…0.26262626… is equivalent to 2699\\frac{26}{99}.<\/p>\n\n\n\n The repeating decimal 0.26262626…0.26262626… is equal to the ratio of integers 2699\\frac{26}{99}. This method, using algebra to eliminate the repeating decimal, is a standard approach for converting repeating decimals into fractions.<\/p>\n","protected":false},"excerpt":{"rendered":" Express the number as a ratio of integers. 0.26 = 0.26262626 . .. The Correct Answer and Explanation is : To express the repeating decimal 0.26262626…0.26262626… as a ratio of integers, we can follow a systematic method. Step 1: Represent the repeating decimal as a variable. Let x=0.26262626…x = 0.26262626…. Notice that the decimal repeats […]<\/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-189503","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/189503","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=189503"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/189503\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=189503"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=189503"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=189503"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Represent the repeating decimal as a variable.<\/h3>\n\n\n\n
Step 2: Multiply both sides by 100.<\/h3>\n\n\n\n
Step 3: Subtract the original equation from this new equation.<\/h3>\n\n\n\n
Step 4: Solve for xx.<\/h3>\n\n\n\n
Verification:<\/h3>\n\n\n\n
Conclusion:<\/h3>\n\n\n\n