{"id":228142,"date":"2025-06-07T03:48:35","date_gmt":"2025-06-07T03:48:35","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=228142"},"modified":"2025-06-07T03:48:37","modified_gmt":"2025-06-07T03:48:37","slug":"express-the-number-0-000216-in-scientific-notation-2-16-x-10-4-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/07\/express-the-number-0-000216-in-scientific-notation-2-16-x-10-4-2\/","title":{"rendered":"Express the number 0.000216 in scientific notation (2.16 x 10^-4)."},"content":{"rendered":"\n

Express the number 0.000216 in scientific notation (2.16 x 10^-4). Express 166,000 in exponential (scientific) notation (1.66 x 10^5). Express the number 8.64 x 10^-3 in common decimal form (0.00864). Express the number 1.16 x 10^4 in common decimal form (11600). How many significant figures are there in the number 0.045607007 (7)<\/p>\n\n\n\n

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

ChatGPT said:<\/h6>\n\n\n\n

Correct Answers:<\/h3>\n\n\n\n
    \n
  1. Scientific notation of 0.000216<\/strong>:
    \u2705 2.16 \u00d7 10\u207b\u2074<\/strong><\/li>\n\n\n\n
  2. Scientific notation of 166,000<\/strong>:
    \u2705 1.66 \u00d7 10\u2075<\/strong><\/li>\n\n\n\n
  3. Decimal form of 8.64 \u00d7 10\u207b\u00b3<\/strong>:
    \u2705 0.00864<\/strong><\/li>\n\n\n\n
  4. Decimal form of 1.16 \u00d7 10\u2074<\/strong>:
    \u2705 11,600<\/strong><\/li>\n\n\n\n
  5. Significant figures in 0.045607007<\/strong>:
    \u2705 7 significant figures<\/strong><\/li>\n<\/ol>\n\n\n\n
    \n\n\n\n

    Explanation:<\/h3>\n\n\n\n

    Scientific notation<\/strong> is a way of expressing very large or very small numbers in a compact form, especially useful in science and engineering. It\u2019s written in the form:
    a\u00d710na \\times 10^na\u00d710n
    where aaa is a number between 1 and 10, and nnn is an integer.<\/p>\n\n\n\n

    Let\u2019s break down each case:<\/p>\n\n\n\n

      \n
    1. 0.000216 \u2192 2.16 \u00d7 10\u207b\u2074<\/strong>:
      Move the decimal point 4 places to the right<\/strong> to get 2.16. Since we made the number bigger, the exponent is negative.<\/li>\n\n\n\n
    2. 166,000 \u2192 1.66 \u00d7 10\u2075<\/strong>:
      Move the decimal point 5 places to the left<\/strong>. We reduce the number\u2019s size, so the exponent is positive.<\/li>\n\n\n\n
    3. 8.64 \u00d7 10\u207b\u00b3 \u2192 0.00864<\/strong>:
      Move the decimal 3 places to the left<\/strong>, as the exponent is negative. This gives the correct decimal.<\/li>\n\n\n\n
    4. 1.16 \u00d7 10\u2074 \u2192 11,600<\/strong>:
      Move the decimal 4 places to the right<\/strong> due to the positive exponent.<\/li>\n<\/ol>\n\n\n\n

      Now, about significant figures<\/strong>:<\/p>\n\n\n\n

      Significant figures are the digits in a number that carry meaningful contributions to its measurement accuracy. Rules include:<\/p>\n\n\n\n

        \n
      • All non-zero digits<\/strong> are significant.<\/li>\n\n\n\n
      • Zeros between non-zero digits<\/strong> are significant.<\/li>\n\n\n\n
      • Leading zeros<\/strong> (zeros before the first non-zero digit) are not<\/strong> significant.<\/li>\n\n\n\n
      • Trailing zeros<\/strong> in a decimal are significant.<\/li>\n<\/ul>\n\n\n\n

        For the number 0.045607007<\/strong>:<\/p>\n\n\n\n

          \n
        • Ignore the leading zeros (0.0).<\/li>\n\n\n\n
        • All the digits after that (4, 5, 6, 0, 7, 0, 0, 7) are significant.<\/li>\n\n\n\n
        • That gives us 7 significant figures<\/strong>.<\/li>\n<\/ul>\n\n\n\n

          Knowing how to work with scientific notation and significant figures is essential for precision in scientific communication and calculations.<\/p>\n\n\n\n

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

          Express the number 0.000216 in scientific notation (2.16 x 10^-4). Express 166,000 in exponential (scientific) notation (1.66 x 10^5). Express the number 8.64 x 10^-3 in common decimal form (0.00864). Express the number 1.16 x 10^4 in common decimal form (11600). How many significant figures are there in the number 0.045607007 (7) The Correct Answer […]<\/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-228142","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228142","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=228142"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228142\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=228142"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=228142"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=228142"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}