{"id":233596,"date":"2025-06-13T08:45:16","date_gmt":"2025-06-13T08:45:16","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=233596"},"modified":"2025-06-13T08:45:19","modified_gmt":"2025-06-13T08:45:19","slug":"solve-the-following-for-x-showing-the-correct-number-of-significant-figures-in-your-answers","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/13\/solve-the-following-for-x-showing-the-correct-number-of-significant-figures-in-your-answers\/","title":{"rendered":"Solve the following for x, showing the correct number of significant figures in your answers"},"content":{"rendered":"\n

Solve the following for x, showing the correct number of significant figures in your answers: 0.0100 * 48.2 = 2.4 * 10^x = (x * log(10.5)) 0.00900 * 20.8 Y – 439 Xo, (o log(0.0660 \/ 9.12) = 0.468 log(295) = (0.05321 * 8.7) 0.488 = (0.003771 * 15.2) 7 * (0.0021 * 72.5) = 0.0509 0.00612 XFoywl 4.60×10^4 = 8.80×10^8.314 * 10^3.75×10^6 = 82.9 * 625 * 305) * 8.314 * 10^623<\/p>\n\n\n\n

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

Let\u2019s tackle each expression<\/strong>, calculate the correct value, and round it properly based on significant figures<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

1. 0.0100 \u00d7 48.2<\/strong><\/h3>\n\n\n\n
    \n
  • Calculation:
    0.0100\u00d748.2=0.4820.0100 \u00d7 48.2 = 0.4820.0100\u00d748.2=0.482<\/li>\n\n\n\n
  • Significant figures: 0.0100 has 3 sig. figs<\/strong>, 48.2 has 3 sig. figs<\/strong> \u2192 answer = 0.482 (3 sig. figs)<\/strong><\/li>\n<\/ul>\n\n\n\n
    \n\n\n\n

    2. 2.4 \u00d7 10^x = (x \u00d7 log(10.5))<\/strong><\/h3>\n\n\n\n

    This is an equation with variables. Rearranged:2.4\u00d710x=x\u00d7log\u2061(10.5)2.4 \u00d7 10^x = x \u00d7 \\log(10.5)2.4\u00d710x=x\u00d7log(10.5)<\/p>\n\n\n\n

    Take logs:log\u2061(2.4\u00d710x)=log\u2061(x\u00d7log\u2061(10.5))\\log(2.4 \u00d7 10^x) = \\log(x \u00d7 \\log(10.5))log(2.4\u00d710x)=log(x\u00d7log(10.5))<\/p>\n\n\n\n

    This becomes:log\u2061(2.4)+x=log\u2061(x)+log\u2061(log\u2061(10.5))\\log(2.4) + x = \\log(x) + \\log(\\log(10.5))log(2.4)+x=log(x)+log(log(10.5))<\/p>\n\n\n\n

    This is transcendental<\/strong> and requires numerical solving. Let\u2019s simplify:<\/p>\n\n\n\n

      \n
    • log\u2061(2.4)\u22480.3802\\log(2.4) \u2248 0.3802log(2.4)\u22480.3802<\/li>\n\n\n\n
    • log\u2061(10.5)\u22481.021\\log(10.5) \u2248 1.021log(10.5)\u22481.021<\/li>\n\n\n\n
    • log\u2061(log\u2061(10.5))\u2248log\u2061(1.021)\u22480.009\\log(\\log(10.5)) \u2248 \\log(1.021) \u2248 0.009log(log(10.5))\u2248log(1.021)\u22480.009<\/li>\n<\/ul>\n\n\n\n

      Try trial-and-error or numerical methods:
      Let\u2019s assume x=1x = 1x=1:
      LHS: 2.4\u00d7101=242.4 \u00d7 10^1 = 242.4\u00d7101=24
      RHS: 1\u00d7log\u2061(10.5)=1.0211 \u00d7 \\log(10.5) = 1.0211\u00d7log(10.5)=1.021 \u2192 not equal
      Try x=15x = 15x=15:
      LHS: 2.4\u00d71015=2.4e152.4 \u00d7 10^{15} = 2.4e152.4\u00d71015=2.4e15
      RHS: 15\u00d71.021=15.31515 \u00d7 1.021 = 15.31515\u00d71.021=15.315<\/p>\n\n\n\n

      Very far. So this is likely symbolic only<\/strong>, or not solvable without context.<\/p>\n\n\n\n

      \n\n\n\n

      3. 0.00900 \u00d7 20.8<\/strong><\/h3>\n\n\n\n
        \n
      • 0.00900\u00d720.8=0.18720.00900 \u00d7 20.8 = 0.18720.00900\u00d720.8=0.1872<\/li>\n\n\n\n
      • Least sig. figs: 0.00900 \u2192 3 sig. figs<\/strong><\/li>\n\n\n\n
      • Final: 0.187 (3 sig. figs)<\/strong><\/li>\n<\/ul>\n\n\n\n
        \n\n\n\n

        4. log(0.0660 \/ 9.12)<\/strong><\/h3>\n\n\n\n
          \n
        • Division: 0.0660\/9.12=0.00723680.0660 \/ 9.12 = 0.00723680.0660\/9.12=0.0072368<\/li>\n\n\n\n
        • Log: log\u2061(0.0072368)\u2248\u22122.140\\log(0.0072368) \u2248 -2.140log(0.0072368)\u2248\u22122.140<\/li>\n\n\n\n
        • Sig. figs in log: 3 sig. figs \u2192 3 decimal places<\/strong><\/li>\n\n\n\n
        • Final: \u22122.140<\/strong><\/li>\n<\/ul>\n\n\n\n
          \n\n\n\n

          5. 0.468 \u00d7 log(295)<\/strong><\/h3>\n\n\n\n
            \n
          • log\u2061(295)\u22482.470\\log(295) \u2248 2.470log(295)\u22482.470<\/li>\n\n\n\n
          • Multiply: 0.468\u00d72.470=1.1560.468 \u00d7 2.470 = 1.1560.468\u00d72.470=1.156<\/li>\n\n\n\n
          • Sig. figs: both 3 \u2192 1.16 (3 sig. figs)<\/strong><\/li>\n<\/ul>\n\n\n\n
            \n\n\n\n

            6. 0.05321 \u00d7 8.7<\/strong><\/h3>\n\n\n\n
              \n
            • 0.05321\u00d78.7=0.4629270.05321 \u00d7 8.7 = 0.4629270.05321\u00d78.7=0.462927<\/li>\n\n\n\n
            • Least sig. figs: 8.7 \u2192 2<\/li>\n\n\n\n
            • Final: 0.46<\/strong><\/li>\n<\/ul>\n\n\n\n
              \n\n\n\n

              7. 0.488 = (0.003771 \u00d7 15.2)<\/strong><\/h3>\n\n\n\n
                \n
              • Right side: 0.003771\u00d715.2=0.05731920.003771 \u00d7 15.2 = 0.05731920.003771\u00d715.2=0.0573192<\/li>\n\n\n\n
              • Final: 0.0573 (3 sig. figs)<\/strong>
                Not equal to 0.488, so equation is false unless context missing.<\/li>\n<\/ul>\n\n\n\n
                \n\n\n\n

                8. 7 \u00d7 (0.0021 \u00d7 72.5)<\/strong><\/h3>\n\n\n\n
                  \n
                • Inside: 0.0021\u00d772.5=0.152250.0021 \u00d7 72.5 = 0.152250.0021\u00d772.5=0.15225<\/li>\n\n\n\n
                • Multiply: 7\u00d70.15225=1.065757 \u00d7 0.15225 = 1.065757\u00d70.15225=1.06575<\/li>\n\n\n\n
                • Sig. figs: 0.0021 (2), 72.5 (3), 7 (1)<\/li>\n\n\n\n
                • 1 sig. fig dominates \u2192 1<\/strong><\/li>\n<\/ul>\n\n\n\n
                  \n\n\n\n

                  9. 0.0509 \u00d7 0.00612<\/strong><\/h3>\n\n\n\n
                    \n
                  • 0.0509\u00d70.00612=0.00031150.0509 \u00d7 0.00612 = 0.00031150.0509\u00d70.00612=0.0003115<\/li>\n\n\n\n
                  • Sig. figs: 3 \u00d7 3 = 3<\/li>\n\n\n\n
                  • Final: 3.12 \u00d7 10\u207b\u2074<\/strong><\/li>\n<\/ul>\n\n\n\n
                    \n\n\n\n

                    10. 4.60\u00d710\u2074 = 8.80\u00d710\u2078.314 \u00d7 10\u00b3.75\u00d710\u2076<\/strong><\/h3>\n\n\n\n

                    Possibly malformed or missing operator between terms. Also, 8.808.3148.80^{8.314}8.808.314 is ~1.49\u00d710\u2078, but the rest is not computable without clear formatting.<\/p>\n\n\n\n

                    \n\n\n\n

                    11. 82.9 \u00d7 625 \u00d7 305 \u00d7 8.314 \u00d7 10\u2076\u00b2\u00b3<\/strong><\/h3>\n\n\n\n

                    That\u2019s:<\/p>\n\n\n\n

                      \n
                    • Multiply constants:
                      82.9\u00d7625\u00d7305\u00d78.314\u22481.315\u00d710882.9 \u00d7 625 \u00d7 305 \u00d7 8.314 \u2248 1.315 \u00d7 10^882.9\u00d7625\u00d7305\u00d78.314\u22481.315\u00d7108<\/li>\n\n\n\n
                    • Final with exponent:
                      \u22481.315\u00d7108\u00d710623=1.315\u00d710631\u2248 1.315 \u00d7 10^8 \u00d7 10^{623} = 1.315 \u00d7 10^{631}\u22481.315\u00d7108\u00d710623=1.315\u00d710631<\/li>\n\n\n\n
                    • Final: 1.32 \u00d7 10^631 (3 sig. figs)<\/strong><\/li>\n<\/ul>\n\n\n\n
                      \n\n\n\n

                      \ud83d\udd0d Summary of Final Answers (with correct significant figures):<\/h2>\n\n\n\n
                      Expression<\/th>Answer<\/th><\/tr><\/thead>
                      0.0100 \u00d7 48.2<\/td>0.482<\/strong><\/td><\/tr>
                      0.00900 \u00d7 20.8<\/td>0.187<\/strong><\/td><\/tr>
                      log(0.0660 \/ 9.12)<\/td>\u22122.140<\/strong><\/td><\/tr>
                      0.468 \u00d7 log(295)<\/td>1.16<\/strong><\/td><\/tr>
                      0.05321 \u00d7 8.7<\/td>0.46<\/strong><\/td><\/tr>
                      0.003771 \u00d7 15.2<\/td>0.0573<\/strong><\/td><\/tr>
                      7 \u00d7 (0.0021 \u00d7 72.5)<\/td>1<\/strong><\/td><\/tr>
                      0.0509 \u00d7 0.00612<\/td>3.12 \u00d7 10\u207b\u2074<\/strong><\/td><\/tr>
                      82.9 \u00d7 625 \u00d7 305 \u00d7 8.314 \u00d7 10\u00b2\u00b3<\/td>1.32 \u00d7 10^631<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
                      \n\n\n\n

                      \ud83d\udcd8 Significant Figures Note:<\/h3>\n\n\n\n
                        \n
                      • Multiplication\/Division<\/strong>: Least number of significant figures<\/strong> among terms.<\/li>\n\n\n\n
                      • Logarithms<\/strong>: Number of decimal places<\/strong> in the result equals the number of significant figures<\/strong> in the original number.<\/li>\n\n\n\n
                      • Maintain clarity with scientific notation for very large or small values.<\/li>\n<\/ul>\n\n\n\n
                        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

                        Solve the following for x, showing the correct number of significant figures in your answers: 0.0100 * 48.2 = 2.4 * 10^x = (x * log(10.5)) 0.00900 * 20.8 Y – 439 Xo, (o log(0.0660 \/ 9.12) = 0.468 log(295) = (0.05321 * 8.7) 0.488 = (0.003771 * 15.2) 7 * (0.0021 * 72.5) = […]<\/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-233596","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233596","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=233596"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233596\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=233596"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=233596"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=233596"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}