{"id":230316,"date":"2025-06-09T06:51:26","date_gmt":"2025-06-09T06:51:26","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=230316"},"modified":"2025-06-09T06:51:39","modified_gmt":"2025-06-09T06:51:39","slug":"significant-digits-and-scientific-notation-part-1-determine-the-number-of-significant-digits-in-each-number-and-write-out-the-specific-significant-digits","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/09\/significant-digits-and-scientific-notation-part-1-determine-the-number-of-significant-digits-in-each-number-and-write-out-the-specific-significant-digits\/","title":{"rendered":"Significant Digits and Scientific Notation Part 1 Determine the number of significant digits in each number and write out the specific significant digits"},"content":{"rendered":"\n

Significant Digits and Scientific Notation Part 1 Determine the number of significant digits in each number and write out the specific significant digits: 405,000 0.0098 39.999999 13.00 80,000,089 55,430.00 0.000033 620.03080 Part 2 Convert each regular number into scientific notation: 70,000,000 0.000000048 67,890,000 70,500 450,900,810<\/p>\n\n\n\n

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

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

Part 1: Significant Digits<\/strong><\/h2>\n\n\n\n

Determine the number of significant digits and identify them:<\/p>\n\n\n\n

    \n
  1. 405,000<\/strong>\n
      \n
    • Significant digits<\/strong>: 3<\/li>\n\n\n\n
    • Digits<\/strong>: 4, 0, 5
      (Trailing zeros are not significant unless there’s a decimal.)<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • 0.0098<\/strong>\n
        \n
      • Significant digits<\/strong>: 2<\/li>\n\n\n\n
      • Digits<\/strong>: 9, 8
        (Leading zeros are not significant.)<\/li>\n<\/ul>\n<\/li>\n\n\n\n
      • 39.999999<\/strong>\n
          \n
        • Significant digits<\/strong>: 8<\/li>\n\n\n\n
        • Digits<\/strong>: 3, 9, 9, 9, 9, 9, 9, 9<\/li>\n<\/ul>\n<\/li>\n\n\n\n
        • 13.00<\/strong>\n
            \n
          • Significant digits<\/strong>: 4<\/li>\n\n\n\n
          • Digits<\/strong>: 1, 3, 0, 0
            (Trailing zeros after decimal are significant.)<\/li>\n<\/ul>\n<\/li>\n\n\n\n
          • 80,000,089<\/strong>\n
              \n
            • Significant digits<\/strong>: 8<\/li>\n\n\n\n
            • Digits<\/strong>: 8, 0, 0, 0, 0, 0, 8, 9<\/li>\n<\/ul>\n<\/li>\n\n\n\n
            • 55,430.00<\/strong>\n
                \n
              • Significant digits<\/strong>: 7<\/li>\n\n\n\n
              • Digits<\/strong>: 5, 5, 4, 3, 0, 0, 0<\/li>\n<\/ul>\n<\/li>\n\n\n\n
              • 0.000033<\/strong>\n
                  \n
                • Significant digits<\/strong>: 2<\/li>\n\n\n\n
                • Digits<\/strong>: 3, 3<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                • 620.03080<\/strong>\n
                    \n
                  • Significant digits<\/strong>: 8<\/li>\n\n\n\n
                  • Digits<\/strong>: 6, 2, 0, 0, 3, 0, 8, 0<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n
                    \n\n\n\n

                    Part 2: Scientific Notation<\/strong><\/h2>\n\n\n\n
                      \n
                    1. 70,000,000,000<\/strong> \u2192 7.0 \u00d7 10\u00b9\u2070<\/strong><\/li>\n\n\n\n
                    2. 0.000000048<\/strong> \u2192 4.8 \u00d7 10\u207b\u2078<\/strong><\/li>\n\n\n\n
                    3. 67,890,000<\/strong> \u2192 6.789 \u00d7 10\u2077<\/strong><\/li>\n\n\n\n
                    4. 70,500<\/strong> \u2192 7.05 \u00d7 10\u2074<\/strong><\/li>\n\n\n\n
                    5. 450,900,800<\/strong> \u2192 4.509008 \u00d7 10\u2078<\/strong><\/li>\n\n\n\n
                    6. 0.000045<\/strong> \u2192 4.5 \u00d7 10\u207b\u2075<\/strong><\/li>\n<\/ol>\n\n\n\n
                      \n\n\n\n

                      Explanation <\/strong><\/h2>\n\n\n\n

                      Significant digits (or significant figures) are the digits in a number that carry meaningful information about its precision. They include all non-zero digits, any zeros between significant digits, and trailing zeros only if they are to the right of a decimal point. Leading zeros are never<\/strong> significant; they simply indicate the position of the decimal point.<\/p>\n\n\n\n

                      For example, in 0.0098<\/strong>, the first two zeros are placeholders and not significant, so only “9” and “8” count. Meanwhile, a number like 13.00<\/strong> includes the trailing zeros as significant because they reflect measured precision.<\/p>\n\n\n\n

                      When dealing with large numbers like 405,000<\/strong>, trailing zeros without<\/strong> a decimal point are considered not<\/strong> significant unless otherwise specified. However, in 55,430.00<\/strong>, the decimal makes the trailing zeros significant because they show the number is measured to that precision.<\/p>\n\n\n\n

                      Scientific notation is a method used to express very large or very small numbers in a compact form. It helps in simplifying calculations and clearly indicating significant digits. To convert a number into scientific notation, move the decimal point so that only one non-zero digit remains to the left of the decimal. The number of places you move the decimal becomes the exponent of 10.<\/p>\n\n\n\n

                      For instance, 67,890,000<\/strong> becomes 6.789 \u00d7 10\u2077<\/strong> because the decimal moves 7 places to the left. For small numbers like 0.000000048<\/strong>, you move the decimal 8 places to the right, so it becomes 4.8 \u00d7 10\u207b\u2078<\/strong>.<\/p>\n\n\n\n

                      Understanding significant digits and scientific notation is essential in science and engineering because they reflect the precision of measurements and help manage very large or small quantities efficiently.<\/p>\n\n\n\n

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

                      Significant Digits and Scientific Notation Part 1 Determine the number of significant digits in each number and write out the specific significant digits: 405,000 0.0098 39.999999 13.00 80,000,089 55,430.00 0.000033 620.03080 Part 2 Convert each regular number into scientific notation: 70,000,000 0.000000048 67,890,000 70,500 450,900,810 The Correct Answer and Explanation is: Part 1: Significant Digits […]<\/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-230316","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230316","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=230316"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230316\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=230316"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=230316"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=230316"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}