{"id":244304,"date":"2025-07-05T03:53:40","date_gmt":"2025-07-05T03:53:40","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=244304"},"modified":"2025-07-05T03:53:42","modified_gmt":"2025-07-05T03:53:42","slug":"convert-the-given-standard-notation-below-to-scientific-notation_","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/05\/convert-the-given-standard-notation-below-to-scientific-notation_\/","title":{"rendered":"Convert the given standard notation below to scientific notation_"},"content":{"rendered":"\n

‘Convert the given standard notation below to scientific notation_ Then, perform the indicated operation. Apply the rules for significant figures in your final answer. 150,000 0.0025 * 20 3,000,000 0.015 X 150’<\/p>\n\n\n\n

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

Let’s break down the problem step by step.<\/p>\n\n\n\n

1. Convert the numbers to scientific notation<\/strong>:<\/h3>\n\n\n\n

We need to express each number in scientific notation.<\/p>\n\n\n\n

    \n
  • 150,000150,000150,000 = 1.5\u00d71051.5 \\times 10^51.5\u00d7105<\/li>\n\n\n\n
  • 0.00250.00250.0025 = 2.5\u00d710\u221232.5 \\times 10^{-3}2.5\u00d710\u22123<\/li>\n\n\n\n
  • 202020 = 2.0\u00d71012.0 \\times 10^12.0\u00d7101 (note that 2.02.02.0 keeps one significant figure)<\/li>\n\n\n\n
  • 3,000,0003,000,0003,000,000 = 3.0\u00d71063.0 \\times 10^63.0\u00d7106 (again, keeping significant figures)<\/li>\n\n\n\n
  • 0.0150.0150.015 = 1.5\u00d710\u221221.5 \\times 10^{-2}1.5\u00d710\u22122<\/li>\n\n\n\n
  • 150150150 = 1.5\u00d71021.5 \\times 10^21.5\u00d7102<\/li>\n<\/ul>\n\n\n\n

    2. Perform the multiplication<\/strong>:<\/h3>\n\n\n\n

    Now we need to multiply all of the numbers in scientific notation. We will multiply the coefficients and add the exponents:(1.5\u00d7105)\u00d7(2.5\u00d710\u22123)\u00d7(2.0\u00d7101)\u00d7(3.0\u00d7106)\u00d7(1.5\u00d710\u22122)\u00d7(1.5\u00d7102)(1.5 \\times 10^5) \\times (2.5 \\times 10^{-3}) \\times (2.0 \\times 10^1) \\times (3.0 \\times 10^6) \\times (1.5 \\times 10^{-2}) \\times (1.5 \\times 10^2)(1.5\u00d7105)\u00d7(2.5\u00d710\u22123)\u00d7(2.0\u00d7101)\u00d7(3.0\u00d7106)\u00d7(1.5\u00d710\u22122)\u00d7(1.5\u00d7102)<\/p>\n\n\n\n

      \n
    • First, multiply the coefficients: 1.5\u00d72.5\u00d72.0\u00d73.0\u00d71.5\u00d71.5=1.5\u00d72.5=3.751.5 \\times 2.5 \\times 2.0 \\times 3.0 \\times 1.5 \\times 1.5 = 1.5 \\times 2.5 = 3.751.5\u00d72.5\u00d72.0\u00d73.0\u00d71.5\u00d71.5=1.5\u00d72.5=3.75 3.75\u00d72.0=7.53.75 \\times 2.0 = 7.53.75\u00d72.0=7.5 7.5\u00d73.0=22.57.5 \\times 3.0 = 22.57.5\u00d73.0=22.5 22.5\u00d71.5=33.7522.5 \\times 1.5 = 33.7522.5\u00d71.5=33.75 33.75\u00d71.5=50.62533.75 \\times 1.5 = 50.62533.75\u00d71.5=50.625<\/li>\n<\/ul>\n\n\n\n

      So the total coefficient is 50.62550.62550.625.<\/p>\n\n\n\n

        \n
      • Now, add the exponents: 105\u00d710\u22123\u00d7101\u00d7106\u00d710\u22122\u00d7102=105\u22123+1+6\u22122+2=10910^5 \\times 10^{-3} \\times 10^1 \\times 10^6 \\times 10^{-2} \\times 10^2 = 10^{5 – 3 + 1 + 6 – 2 + 2} = 10^9105\u00d710\u22123\u00d7101\u00d7106\u00d710\u22122\u00d7102=105\u22123+1+6\u22122+2=109<\/li>\n<\/ul>\n\n\n\n

        3. Combine the coefficient and exponent<\/strong>:<\/h3>\n\n\n\n

        50.625\u00d710950.625 \\times 10^950.625\u00d7109<\/p>\n\n\n\n

        4. Adjust the coefficient<\/strong>:<\/h3>\n\n\n\n

        In scientific notation, the coefficient should be between 1 and 10. We can adjust 50.62550.62550.625 as follows:50.625=5.0625\u00d710150.625 = 5.0625 \\times 10^150.625=5.0625\u00d7101<\/p>\n\n\n\n

        So, the final expression becomes:5.0625\u00d7101+9=5.0625\u00d710105.0625 \\times 10^{1 + 9} = 5.0625 \\times 10^{10}5.0625\u00d7101+9=5.0625\u00d71010<\/p>\n\n\n\n

        5. Apply significant figures<\/strong>:<\/h3>\n\n\n\n

        We must apply the correct number of significant figures based on the initial values. The number with the least significant figures is 0.00250.00250.0025 which has 2 significant figures. So, we round our final result to 2 significant figures:5.0625\u22485.15.0625 \\approx 5.15.0625\u22485.1<\/p>\n\n\n\n

        Thus, the final answer in scientific notation is:5.1\u00d710105.1 \\times 10^{10}5.1\u00d71010<\/p>\n\n\n\n

        Conclusion:<\/h3>\n\n\n\n

        The correct final answer, with appropriate significant figures, is:5.1\u00d71010\\boxed{5.1 \\times 10^{10}}5.1\u00d71010\u200b<\/p>\n\n\n\n

        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        ‘Convert the given standard notation below to scientific notation_ Then, perform the indicated operation. Apply the rules for significant figures in your final answer. 150,000 0.0025 * 20 3,000,000 0.015 X 150’ The Correct Answer and Explanation is: Let’s break down the problem step by step. 1. Convert the numbers to scientific notation: We need […]<\/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-244304","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/244304","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=244304"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/244304\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=244304"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=244304"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=244304"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}