{"id":227327,"date":"2025-06-06T04:54:52","date_gmt":"2025-06-06T04:54:52","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=227327"},"modified":"2025-06-06T04:54:54","modified_gmt":"2025-06-06T04:54:54","slug":"write-78982468-in-scientific-notation-rounded-off-to-3-significant-figures","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/06\/write-78982468-in-scientific-notation-rounded-off-to-3-significant-figures\/","title":{"rendered":"Write 78,982,468 in scientific notation rounded off to 3 significant figures"},"content":{"rendered":"\n

1) Write 78,982,468 in scientific notation rounded off to 3 significant figures. A)
B)
C)
D)
E) None of the above 2) Perform the following calculation and round your answer to the correct number of significant figures:
A) 111.0 B) 111.05 C) 111.1 D) 111.10 E) 111.051 F) None of the above 3) Water is 88.8% oxygen by mass. What mass of water contains 77.7 g of oxygen? Make sure to show your math work, if you want to receive credit. A) 69.0 g B) 87.5 g C)
g D)
g E) None of the above 4) The speed of light is
m\/s. Convert this to feet per nanosecond (ft\/ns). Make sure to show your math work, if you want to receive credit. Useful unit equation: 1.000 meter = 3.281 ft A)
ft\/ns B) 0.0914 ft\/ns C) 0.984 ft\/ns D)
ft\/ns E) None of the above<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

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

Let’s go through each of the four questions in the image and solve them with proper math and explanation.<\/p>\n\n\n\n

\n\n\n\n

1) Scientific Notation of 78,982,468 rounded to 3 significant figures<\/strong><\/h3>\n\n\n\n

Step-by-step:<\/strong><\/p>\n\n\n\n

    \n
  • Identify the first three significant figures: 7, 8, and 9.<\/li>\n\n\n\n
  • Convert to scientific notation: 78,982,468\u22487.90\u00d710778,982,468 \\approx 7.90 \\times 10^7<\/li>\n<\/ul>\n\n\n\n

    Answer: B) 7.90 \u00d7 10\u2077<\/strong><\/p>\n\n\n\n

    \n\n\n\n

    2) 91.421 + 19.63 rounded to correct sig figs<\/strong><\/h3>\n\n\n\n

    Step-by-step:<\/strong><\/p>\n\n\n\n

      \n
    • Add the numbers:
      91.421+19.63=111.05191.421 + 19.63 = 111.051<\/li>\n\n\n\n
    • Decimal places rule: Round to the least number of decimal places<\/em>.
      91.421 has 3 decimals, 19.63 has 2 \u2192 round to 2 decimals<\/strong><\/li>\n<\/ul>\n\n\n\n

      Final result: 111.05<\/strong><\/p>\n\n\n\n

      Answer: B) 111.05<\/strong><\/p>\n\n\n\n

      \n\n\n\n

      3) Mass of water for 77.7 g of oxygen (88.8% O\u2082)<\/strong><\/h3>\n\n\n\n

      Step-by-step:<\/strong><\/p>\n\n\n\n

        \n
      • Let the mass of water = xx<\/li>\n\n\n\n
      • Since water is 88.8% oxygen by mass: 0.888x=77.7\u21d2x=77.70.888\u224887.5\u2009g0.888x = 77.7 \\Rightarrow x = \\frac{77.7}{0.888} \\approx 87.5 \\, \\text{g}<\/li>\n<\/ul>\n\n\n\n

        Answer: B) 87.5 g<\/strong><\/p>\n\n\n\n

        \n\n\n\n

        4) Convert 3.00 \u00d7 10\u2078 m\/s to ft\/ns<\/strong><\/h3>\n\n\n\n

        Step-by-step:<\/strong><\/p>\n\n\n\n

          \n
        • 1 meter = 3.281 ft<\/li>\n\n\n\n
        • 1 nanosecond = 10\u2212910^{-9} seconds<\/li>\n<\/ul>\n\n\n\n

          Convert m\/s to ft\/ns: 3.00\u00d7108\u2009m\/s\u00d73.281\u2009ft1\u2009m\u00d71\u2009s109\u2009ns=3.00\u00d7108\u00d73.281109\u22480.984\u2009ft\/ns3.00 \\times 10^8 \\, \\text{m\/s} \\times \\frac{3.281 \\, \\text{ft}}{1 \\, \\text{m}} \\times \\frac{1 \\, \\text{s}}{10^9 \\, \\text{ns}} = \\frac{3.00 \\times 10^8 \\times 3.281}{10^9} \\approx 0.984 \\, \\text{ft\/ns}<\/p>\n\n\n\n

          Answer: C) 0.984 ft\/ns<\/strong><\/p>\n\n\n\n

          \n\n\n\n

          \u2705 Final Answers:<\/strong><\/h3>\n\n\n\n
            \n
          1. B<\/strong><\/li>\n\n\n\n
          2. B<\/strong><\/li>\n\n\n\n
          3. B<\/strong><\/li>\n\n\n\n
          4. C<\/strong><\/li>\n<\/ol>\n\n\n\n
            \n\n\n\n

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

            These problems test key scientific and mathematical skills. Question 1 focuses on scientific notation, which is used to express large numbers concisely. The number 78,982,468 rounded to 3 significant figures becomes 7.90 \u00d7 10\u2077, where trailing zero holds significance.<\/p>\n\n\n\n

            Question 2 emphasizes the rules of significant figures in addition<\/strong>. When adding or subtracting, the result is limited by the least number of decimal places in the operands. 91.421 (3 decimals) + 19.63 (2 decimals) = 111.051, rounded to 2 decimal places<\/strong> gives 111.05.<\/p>\n\n\n\n

            In Question 3, a percentage problem is used to reverse-engineer the total mass based on a part (oxygen). Knowing that water is 88.8% oxygen allows us to set up an equation and solve for the whole. The simple algebra yields 87.5 g of water for 77.7 g of oxygen.<\/p>\n\n\n\n

            Question 4 integrates unit conversions with scientific notation. Speed of light is 3.00 \u00d7 10\u2078 m\/s. Converting meters to feet (using 3.281 ft\/m) and seconds to nanoseconds (1 ns = 10\u207b\u2079 s) leads to a multiplication and division: 3.00\u00d7108\u00d73.281\/109=0.984\u2009ft\/ns3.00 \\times 10^8 \\times 3.281 \/ 10^9 = 0.984 \\, \\text{ft\/ns}<\/p>\n\n\n\n

            These problems together highlight practical applications of scientific notation, significant figures, proportions, and unit conversions\u2014all vital skills in science and engineering.<\/p>\n\n\n\n

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

            1) Write 78,982,468 in scientific notation rounded off to 3 significant figures. A)B)C)D)E) None of the above 2) Perform the following calculation and round your answer to the correct number of significant figures:A) 111.0 B) 111.05 C) 111.1 D) 111.10 E) 111.051 F) None of the above 3) Water is 88.8% oxygen by mass. What […]<\/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-227327","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/227327","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=227327"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/227327\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=227327"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=227327"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=227327"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}