{"id":259972,"date":"2025-07-19T06:43:44","date_gmt":"2025-07-19T06:43:44","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=259972"},"modified":"2025-07-19T06:43:47","modified_gmt":"2025-07-19T06:43:47","slug":"addition-and-subtraction-2-5","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/19\/addition-and-subtraction-2-5\/","title":{"rendered":"Addition and Subtraction 2 5."},"content":{"rendered":"\n

Chapter 3 Addition and Subtraction 2 5.a. For each of the following decimals, show how to write the decimal as a fraction by first put- ting the decimal in expanded form: i. 2.34 ii. 124.5 iii. 7.938 b. Based on your results in part (a), describe a quick way to rewrite a finite decimal as a frac- tion. Illustrate with the example 2748.963<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Writing the Decimals as Fractions in Expanded Form:<\/h3>\n\n\n\n

i. 2.34<\/strong><\/p>\n\n\n\n

    \n
  1. Break the decimal down into expanded form: 2.34=2+310+41002.34 = 2 + \\frac{3}{10} + \\frac{4}{100}2.34=2+103\u200b+1004\u200b<\/li>\n\n\n\n
  2. Now, combine the terms into a single fraction: 2.34=2341002.34 = \\frac{234}{100}2.34=100234\u200b The fraction is 234100\\frac{234}{100}100234\u200b, which can be simplified by dividing both the numerator and the denominator by 2: 234100=11750\\frac{234}{100} = \\frac{117}{50}100234\u200b=50117\u200b<\/li>\n<\/ol>\n\n\n\n

    ii. 124.5<\/strong><\/p>\n\n\n\n

      \n
    1. Break the decimal down into expanded form: 124.5=124+510124.5 = 124 + \\frac{5}{10}124.5=124+105\u200b<\/li>\n\n\n\n
    2. Now, combine the terms into a single fraction: 124.5=124510124.5 = \\frac{1245}{10}124.5=101245\u200b This fraction is already in its simplest form.<\/li>\n<\/ol>\n\n\n\n

      iii. 7.938<\/strong><\/p>\n\n\n\n

        \n
      1. Break the decimal down into expanded form: 7.938=7+910+3100+810007.938 = 7 + \\frac{9}{10} + \\frac{3}{100} + \\frac{8}{1000}7.938=7+109\u200b+1003\u200b+10008\u200b<\/li>\n\n\n\n
      2. Now, combine the terms into a single fraction: 7.938=793810007.938 = \\frac{7938}{1000}7.938=10007938\u200b This fraction is already in its simplest form, as the greatest common divisor (GCD) of 7938 and 1000 is 2: 79381000=3969500\\frac{7938}{1000} = \\frac{3969}{500}10007938\u200b=5003969\u200b<\/li>\n<\/ol>\n\n\n\n

        (b) Quick Way to Rewrite a Finite Decimal as a Fraction:<\/h3>\n\n\n\n

        A quick way<\/strong> to rewrite a finite decimal as a fraction is to:<\/p>\n\n\n\n

          \n
        1. Remove the decimal point<\/strong> by multiplying both the numerator and denominator by a power of 10 such that the decimal point moves to the rightmost position. The number of places you move the decimal point determines the power of 10.<\/li>\n\n\n\n
        2. Simplify<\/strong> the resulting fraction if possible.<\/li>\n<\/ol>\n\n\n\n

          Example: 2748.963<\/strong><\/p>\n\n\n\n

            \n
          1. Rewrite the decimal in expanded form: 2748.963=2748+910+6100+310002748.963 = 2748 + \\frac{9}{10} + \\frac{6}{100} + \\frac{3}{1000}2748.963=2748+109\u200b+1006\u200b+10003\u200b<\/li>\n\n\n\n
          2. Combine the terms: 2748.963=274896310002748.963 = \\frac{2748963}{1000}2748.963=10002748963\u200b<\/li>\n\n\n\n
          3. This fraction is already in its simplest form as 2748963 and 1000 do not have a common factor.<\/li>\n<\/ol>\n\n\n\n

            Thus, the decimal 2748.963 is written as the fraction 27489631000\\frac{2748963}{1000}10002748963\u200b.<\/p>\n\n\n\n

            In general, to convert a decimal to a fraction:<\/p>\n\n\n\n

              \n
            • Count the number of digits after the decimal point.<\/li>\n\n\n\n
            • Multiply the decimal by 10n10^n10n (where nnn is the number of digits after the decimal point) to shift the decimal place.<\/li>\n\n\n\n
            • Write the resulting number over the corresponding power of 10 and simplify if necessary.<\/li>\n<\/ul>\n\n\n\n
              \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

              Chapter 3 Addition and Subtraction 2 5.a. For each of the following decimals, show how to write the decimal as a fraction by first put- ting the decimal in expanded form: i. 2.34 ii. 124.5 iii. 7.938 b. Based on your results in part (a), describe a quick way to rewrite a finite decimal as […]<\/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-259972","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/259972","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=259972"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/259972\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=259972"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=259972"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=259972"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}