{"id":236155,"date":"2025-06-16T05:29:18","date_gmt":"2025-06-16T05:29:18","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=236155"},"modified":"2025-06-16T05:29:20","modified_gmt":"2025-06-16T05:29:20","slug":"3-5-x-10-3-x-10%c2%b9-express-your-answer-in-scientific-notation","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/16\/3-5-x-10-3-x-10%c2%b9-express-your-answer-in-scientific-notation\/","title":{"rendered":"(3.5 \u00d7 10??) (3 \u00d7 10?\u00b9?) Express your answer in scientific notation."},"content":{"rendered":"\n

(3.5 \u00d7 10??) (3 \u00d7 10?\u00b9?) Express your answer in scientific notation. 1.05 \u00d7 10?\u00b9? 1.05 \u00d7 10?\u00b9? 1.05 \u00d7 10?\u00b9\u00b3 1.05 \u00d7 10\u00b9?<\/p>\n\n\n\n

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

Correct Answer:<\/h3>\n\n\n\n

1.05 \u00d7 10\u207b\u00b9\u00b3<\/strong><\/p>\n\n\n\n

\n\n\n\n

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

Scientific notation is a method of expressing numbers that are too large or too small to be conveniently written in decimal form. It uses powers of 10 to simplify these expressions. In this case, the problem involves multiplying two numbers written in scientific notation: (3.5\u00d710?)\u00d7(3\u00d710\u221214)(3.5 \u00d7 10^?) \u00d7 (3 \u00d7 10^{-14})(3.5\u00d710?)\u00d7(3\u00d710\u221214)<\/p>\n\n\n\n

Assume the missing exponent in the first number is 1, as suggested by the answer options. This makes the expression: (3.5\u00d7101)\u00d7(3\u00d710\u221214)(3.5 \u00d7 10^1) \u00d7 (3 \u00d7 10^{-14})(3.5\u00d7101)\u00d7(3\u00d710\u221214)<\/p>\n\n\n\n

Multiplication in scientific notation follows two steps:<\/p>\n\n\n\n

    \n
  1. Multiply the decimal numbers: 3.5\u00d73=10.53.5 \u00d7 3 = 10.53.5\u00d73=10.5<\/li>\n\n\n\n
  2. Add the exponents of 10: 101\u00d710\u221214=10(1+(\u221214))=10\u22121310^1 \u00d7 10^{-14} = 10^{(1 + (-14))} = 10^{-13}101\u00d710\u221214=10(1+(\u221214))=10\u221213<\/li>\n<\/ol>\n\n\n\n

    So the result becomes: 10.5\u00d710\u22121310.5 \u00d7 10^{-13}10.5\u00d710\u221213<\/p>\n\n\n\n

    However, in scientific notation, the number before the power of 10 should be between 1 and 10. Since 10.5 is greater than 10, it needs to be adjusted. Dividing 10.5 by 10 gives 1.05, and increasing the exponent by 1 keeps the value unchanged: 10.5\u00d710\u221213=1.05\u00d710\u22121210.5 \u00d7 10^{-13} = 1.05 \u00d7 10^{-12}10.5\u00d710\u221213=1.05\u00d710\u221212<\/p>\n\n\n\n

    But none of the choices show 1.05\u00d710\u2212121.05 \u00d7 10^{-12}1.05\u00d710\u221212. Let\u2019s recheck the assumed exponent in the first number. Try assuming the first exponent is -1<\/strong> instead: (3.5\u00d710\u22121)\u00d7(3\u00d710\u221214)=10.5\u00d710\u221215=1.05\u00d710\u221214(3.5 \u00d7 10^{-1}) \u00d7 (3 \u00d7 10^{-14}) = 10.5 \u00d7 10^{-15} = 1.05 \u00d7 10^{-14}(3.5\u00d710\u22121)\u00d7(3\u00d710\u221214)=10.5\u00d710\u221215=1.05\u00d710\u221214<\/p>\n\n\n\n

    Still doesn\u2019t match.<\/p>\n\n\n\n

    Now try exponent 0<\/strong>: (3.5\u00d7100)\u00d7(3\u00d710\u221214)=10.5\u00d710\u221214=1.05\u00d710\u221213(3.5 \u00d7 10^0) \u00d7 (3 \u00d7 10^{-14}) = 10.5 \u00d7 10^{-14} = 1.05 \u00d7 10^{-13}(3.5\u00d7100)\u00d7(3\u00d710\u221214)=10.5\u00d710\u221214=1.05\u00d710\u221213<\/p>\n\n\n\n

    Now the expression fits a valid scientific format and matches an answer choice.<\/p>\n\n\n\n

    Thus, the correct answer is:
    1.05 \u00d7 10\u207b\u00b9\u00b3<\/strong>.<\/p>\n\n\n\n

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

    (3.5 \u00d7 10??) (3 \u00d7 10?\u00b9?) Express your answer in scientific notation. 1.05 \u00d7 10?\u00b9? 1.05 \u00d7 10?\u00b9? 1.05 \u00d7 10?\u00b9\u00b3 1.05 \u00d7 10\u00b9? The Correct Answer and Explanation is: Correct Answer: 1.05 \u00d7 10\u207b\u00b9\u00b3 Explanation Scientific notation is a method of expressing numbers that are too large or too small to be conveniently written […]<\/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-236155","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/236155","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=236155"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/236155\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=236155"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=236155"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=236155"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}