{"id":168041,"date":"2024-11-16T16:40:58","date_gmt":"2024-11-16T16:40:58","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=168041"},"modified":"2024-11-16T16:41:01","modified_gmt":"2024-11-16T16:41:01","slug":"without-using-a-calculator-work-out-9-15-x-10-%c2%b92-4-23-x-10-5","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/16\/without-using-a-calculator-work-out-9-15-x-10-%c2%b92-4-23-x-10-5\/","title":{"rendered":"Without Using a calculator, work out (9.15 x 10-\u00b92) (4.23 \u00d7 10-5)"},"content":{"rendered":"\n<p>Without Using a calculator, work out (9.15 x 10-\u00b92) (4.23 \u00d7 10-5)<br>Give your answer in standard form to 3 significant figures.<br>Answer<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To solve the expression (9.15\u00d710\u221212)(4.23\u00d710\u22125)(9.15 \\times 10^{-12})(4.23 \\times 10^{-5})(9.15\u00d710\u221212)(4.23\u00d710\u22125) and express the result in standard form to three significant figures, we can break it down into a few steps:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Multiply the significant figures.<\/h3>\n\n\n\n<p>The first part of the expression involves multiplying the decimal numbers:9.15\u00d74.239.15 \\times 4.239.15\u00d74.23<\/p>\n\n\n\n<p>To simplify, we can estimate this multiplication:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>9.15\u224899.15 \\approx 99.15\u22489 and 4.23\u224844.23 \\approx 44.23\u22484<\/li>\n\n\n\n<li>Multiply 9\u00d74=369 \\times 4 = 369\u00d74=36<\/li>\n<\/ul>\n\n\n\n<p>However, to be more precise, let&#8217;s calculate it without rounding:9.15\u00d74.23=38.83459.15 \\times 4.23 = 38.83459.15\u00d74.23=38.8345<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Add the exponents.<\/h3>\n\n\n\n<p>The second part of the expression involves multiplying the powers of 10:10\u221212\u00d710\u2212510^{-12} \\times 10^{-5}10\u221212\u00d710\u22125<\/p>\n\n\n\n<p>When multiplying powers of 10, you add the exponents:10\u221212\u00d710\u22125=10\u221212+(\u22125)=10\u22121710^{-12} \\times 10^{-5} = 10^{-12 + (-5)} = 10^{-17}10\u221212\u00d710\u22125=10\u221212+(\u22125)=10\u221217<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Combine the results.<\/h3>\n\n\n\n<p>Now, we combine the result from Step 1 with the result from Step 2:(9.15\u00d74.23)\u00d710\u221212\u00d710\u22125=38.8345\u00d710\u221217(9.15 \\times 4.23) \\times 10^{-12} \\times 10^{-5} = 38.8345 \\times 10^{-17}(9.15\u00d74.23)\u00d710\u221212\u00d710\u22125=38.8345\u00d710\u221217<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Convert to standard form.<\/h3>\n\n\n\n<p>To express the result in standard form, we need the decimal number to be between 1 and 10.38.8345=3.88345\u00d710138.8345 = 3.88345 \\times 10^138.8345=3.88345\u00d7101<\/p>\n\n\n\n<p>So:38.8345\u00d710\u221217=3.88345\u00d7101\u00d710\u221217=3.88345\u00d710\u22121638.8345 \\times 10^{-17} = 3.88345 \\times 10^1 \\times 10^{-17} = 3.88345 \\times 10^{-16}38.8345\u00d710\u221217=3.88345\u00d7101\u00d710\u221217=3.88345\u00d710\u221216<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 5: Round to three significant figures.<\/h3>\n\n\n\n<p>Finally, we round the result to three significant figures:3.88345\u22483.883.88345 \\approx 3.883.88345\u22483.88<\/p>\n\n\n\n<p>Thus, the answer in standard form to three significant figures is:3.88\u00d710\u221216\\boxed{3.88 \\times 10^{-16}}3.88\u00d710\u221216\u200b<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Summary:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Multiply the significant figures: 9.15\u00d74.23=38.83459.15 \\times 4.23 = 38.83459.15\u00d74.23=38.8345.<\/li>\n\n\n\n<li>Add the exponents: 10\u221212\u00d710\u22125=10\u22121710^{-12} \\times 10^{-5} = 10^{-17}10\u221212\u00d710\u22125=10\u221217.<\/li>\n\n\n\n<li>Combine the two parts: 38.8345\u00d710\u221217=3.88\u00d710\u22121638.8345 \\times 10^{-17} = 3.88 \\times 10^{-16}38.8345\u00d710\u221217=3.88\u00d710\u221216.<\/li>\n\n\n\n<li>Round the result to three significant figures: 3.88\u00d710\u2212163.88 \\times 10^{-16}3.88\u00d710\u221216.<\/li>\n<\/ol>\n\n\n\n<p>The final result is 3.88\u00d710\u2212163.88 \\times 10^{-16}3.88\u00d710\u221216.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Without Using a calculator, work out (9.15 x 10-\u00b92) (4.23 \u00d7 10-5)Give your answer in standard form to 3 significant figures.Answer The Correct Answer and Explanation is: To solve the expression (9.15\u00d710\u221212)(4.23\u00d710\u22125)(9.15 \\times 10^{-12})(4.23 \\times 10^{-5})(9.15\u00d710\u221212)(4.23\u00d710\u22125) and express the result in standard form to three significant figures, we can break it down into a few [&hellip;]<\/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 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