{"id":186990,"date":"2025-01-31T07:15:32","date_gmt":"2025-01-31T07:15:32","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=186990"},"modified":"2025-01-31T07:15:34","modified_gmt":"2025-01-31T07:15:34","slug":"scientific-notation-worksheet","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/31\/scientific-notation-worksheet\/","title":{"rendered":"\u00a0SCIENTIFIC NOTATION WORKSHEET"},"content":{"rendered":"\n

\u00a0SCIENTIFIC NOTATION WORKSHEET #1 CHANGE EACH OF THE FOLLOWING COMMON NUMBERS INTO PROPER SCIENTIFIC NOTATION 93,000,000 mi. – 9.3×10 m distance to the sun 2. 130,000,000 km – 13 x 10 K _distance to the sun 58,666,000,000,000 mi – 58.Chexib distance to the nearest star 300,000,000 m\/sec = 3 x US speed of light 600,000,000,000,000,000,000,000 – 609 molecules in 2g hydrogen 0.000000027 m-_2.11n diameter of an atom 0.0000010 km – length of one mm 350,000,000 – _ 3.5 VD number of people in USA 9. 0.000000010001 = a single dollars part of national debt 10. 365 days in a year CHANGE EACH OF THE FOLLOWING SCIENTIFIC NUMBERS INTO COMMON NUMBERS 11. 3.6 X 10- 0.000026 12. 7.7 X 102 0.000000000077 13. 9.3 X 10 – 43poopoo 14. 6.0 X 10 – 15. 3.2 X 10% = 0.00032 16. 6.8 X 10&#39;-69 MULTIPLY EACH OF THE FOLLOWING MEASUREMENTS USING PROPER SCIENTIFIC NOTATION: 17. (1.8 x 10g)(3.6 x 10g) – 18. (4.7 x 109 m)(5.5 x 10 sec) – 19. (3.0 x 10&#39; mm)4.0 x 10 mm)(1.2 x 10mm) DIVIDE EACH OF THE FOLLOWING PRORLES GIVING YOUR ANSWERS IN PROPER SCIENTIFIC NOTATION: 20. 4×102- 2 x 10 21. – 4x 10 2 x 1012 2x 10- 4x 1012 23. 6x 10 2 x 10* = ADD OR SUBTRACT EACH OF THE FOLLOWING PROBLEMS AND GIVE YOUR ANSWERS IN PROPER SCIENTIFIC NOTATION 24. 6.3 x 10 + 4.2 x 10 25. 3.32 x 10 -5.00 x 10<\/p>\n\n\n\n

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

Here are the correct answers to your Scientific Notation Worksheet #1<\/strong>, along with a 300-word explanation of how scientific notation works:<\/p>\n\n\n\n

Conversion of Common Numbers to Scientific Notation<\/strong><\/h3>\n\n\n\n
    \n
  1. 93,000,000 mi<\/strong> \u2192 9.3 \u00d7 10\u2077 mi<\/strong><\/li>\n\n\n\n
  2. 130,000,000 km<\/strong> \u2192 1.3 \u00d7 10\u2078 km<\/strong><\/li>\n\n\n\n
  3. 58,666,000,000,000 mi<\/strong> \u2192 5.8666 \u00d7 10\u00b9\u00b3 mi<\/strong><\/li>\n\n\n\n
  4. 300,000,000 m\/sec<\/strong> \u2192 3.0 \u00d7 10\u2078 m\/sec<\/strong><\/li>\n\n\n\n
  5. 600,000,000,000,000,000,000,000 molecules<\/strong> \u2192 6.0 \u00d7 10\u00b2\u00b3 molecules<\/strong><\/li>\n\n\n\n
  6. 0.000000027 m<\/strong> \u2192 2.7 \u00d7 10\u207b\u2078 m<\/strong><\/li>\n\n\n\n
  7. 0.0000010 km<\/strong> \u2192 1.0 \u00d7 10\u207b\u2076 km<\/strong><\/li>\n\n\n\n
  8. 350,000,000<\/strong> \u2192 3.5 \u00d7 10\u2078<\/strong><\/li>\n\n\n\n
  9. 0.000000010001<\/strong> \u2192 1.0001 \u00d7 10\u207b\u2078<\/strong><\/li>\n\n\n\n
  10. 365 days<\/strong> (already in standard notation)<\/li>\n<\/ol>\n\n\n\n

    Conversion of Scientific Notation to Common Numbers<\/strong><\/h3>\n\n\n\n
      \n
    1. 3.6 \u00d7 10\u207b\u2076<\/strong> \u2192 0.0000036<\/strong><\/li>\n\n\n\n
    2. 7.7 \u00d7 10\u00b2<\/strong> \u2192 770<\/strong><\/li>\n\n\n\n
    3. 9.3 \u00d7 10\u2074<\/strong> \u2192 93,000<\/strong><\/li>\n\n\n\n
    4. 6.0 \u00d7 10\u207b\u00b9<\/strong> \u2192 0.6<\/strong><\/li>\n\n\n\n
    5. 3.2 \u00d7 10\u207b\u00b3<\/strong> \u2192 0.0032<\/strong><\/li>\n\n\n\n
    6. 6.8 \u00d7 10\u207b\u2079<\/strong> \u2192 0.0000000068<\/strong><\/li>\n<\/ol>\n\n\n\n

      Multiplication Using Scientific Notation<\/strong><\/h3>\n\n\n\n
        \n
      1. (1.8 \u00d7 10\u2079) \u00d7 (3.6 \u00d7 10\u2079)<\/strong>
        = 6.48 \u00d7 10\u00b9\u2078<\/strong><\/li>\n\n\n\n
      2. (4.7 \u00d7 10\u2079 m) \u00d7 (5.5 \u00d7 10\u2076 sec)<\/strong>
        = 2.585 \u00d7 10\u00b9\u2076 m\u00b7s<\/strong><\/li>\n\n\n\n
      3. (3.0 \u00d7 10\u00b3 mm) \u00d7 (4.0 \u00d7 10\u00b2 mm) \u00d7 (1.2 \u00d7 10\u00b9 mm)<\/strong>
        = 1.44 \u00d7 10\u2077 mm\u00b3<\/strong><\/li>\n<\/ol>\n\n\n\n

        Division Using Scientific Notation<\/strong><\/h3>\n\n\n\n
          \n
        1. (4 \u00d7 10\u00b2) \u00f7 (2 \u00d7 10\u00b9)<\/strong>
          = 2 \u00d7 10\u00b9<\/strong><\/li>\n\n\n\n
        2. (4 \u00d7 10\u207b\u2076) \u00f7 (2 \u00d7 10\u00b9\u00b2)<\/strong>
          = 2 \u00d7 10\u207b\u00b9\u2078<\/strong><\/li>\n\n\n\n
        3. (2 \u00d7 10\u207b\u2074) \u00f7 (4 \u00d7 10\u00b9\u00b2)<\/strong>
          = 5 \u00d7 10\u207b\u00b9\u2077<\/strong><\/li>\n\n\n\n
        4. (6 \u00d7 10\u2076) \u00f7 (2 \u00d7 10\u2074)<\/strong>
          = 3 \u00d7 10\u00b2<\/strong><\/li>\n<\/ol>\n\n\n\n

          Addition & Subtraction Using Scientific Notation<\/strong><\/h3>\n\n\n\n
            \n
          1. (6.3 \u00d7 10\u2075) + (4.2 \u00d7 10\u2075)<\/strong>
            = 1.05 \u00d7 10\u2076<\/strong><\/li>\n\n\n\n
          2. (3.32 \u00d7 10\u00b3) – (5.00 \u00d7 10\u00b2)<\/strong>
            = 2.82 \u00d7 10\u00b3<\/strong><\/li>\n<\/ol>\n\n\n\n
            \n\n\n\n

            Explanation of Scientific Notation (300 Words)<\/strong><\/h3>\n\n\n\n

            Scientific notation is a way of expressing very large or very small numbers in a compact form, making calculations easier, especially in science and engineering. It consists of a number (called the coefficient<\/strong>) between 1 and 10<\/strong>, multiplied by 10 raised to an exponent<\/strong> (power of ten<\/strong>).<\/p>\n\n\n\n

            For example, 93,000,000<\/strong> is written as 9.3 \u00d7 10\u2077<\/strong>, because we move the decimal 7 places to the left<\/strong>. Similarly, 0.0000010<\/strong> is written as 1.0 \u00d7 10\u207b\u2076<\/strong>, because we move the decimal 6 places to the right<\/strong>.<\/p>\n\n\n\n

            In multiplication<\/strong>, the coefficients are multiplied, and exponents are added<\/strong>:
            [
            (3 \u00d7 10\u2074) \u00d7 (2 \u00d7 10\u00b3) = 6 \u00d7 10\u2077
            ]
            In division<\/strong>, the coefficients are divided, and exponents are subtracted<\/strong>:
            [
            (8 \u00d7 10\u2076) \u00f7 (2 \u00d7 10\u00b3) = 4 \u00d7 10\u00b3
            ]
            For addition or subtraction<\/strong>, numbers must have the same exponent<\/strong> before performing the operation. For example,
            [
            (6.3 \u00d7 10\u2075) + (4.2 \u00d7 10\u2075) = 1.05 \u00d7 10\u2076
            ]
            because the exponents match.<\/p>\n\n\n\n

            Scientific notation is widely used in physics, chemistry, and astronomy to simplify working with extremely large or small values, such as the speed of light (3.0 \u00d7 10\u2078 m\/s)<\/strong> or the charge of an electron (1.6 \u00d7 10\u207b\u00b9\u2079 C)<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"

            \u00a0SCIENTIFIC NOTATION WORKSHEET #1 CHANGE EACH OF THE FOLLOWING COMMON NUMBERS INTO PROPER SCIENTIFIC NOTATION 93,000,000 mi. – 9.3×10 m distance to the sun 2. 130,000,000 km – 13 x 10 K _distance to the sun 58,666,000,000,000 mi – 58.Chexib distance to the nearest star 300,000,000 m\/sec = 3 x US speed of light 600,000,000,000,000,000,000,000 […]<\/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-186990","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/186990","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=186990"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/186990\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=186990"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=186990"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=186990"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}