{"id":232496,"date":"2025-06-12T01:59:51","date_gmt":"2025-06-12T01:59:51","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=232496"},"modified":"2025-06-12T01:59:53","modified_gmt":"2025-06-12T01:59:53","slug":"which-is-the-best-estimate-for-frac8-9-times-1083-3-times-104-written-in-scientific-notation","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/12\/which-is-the-best-estimate-for-frac8-9-times-1083-3-times-104-written-in-scientific-notation\/","title":{"rendered":"Which is the best estimate for \\frac{(8.9 \\times 10^8)}{(3.3 \\times 10^4)} written in scientific notation"},"content":{"rendered":"\n

Which is the best estimate for \\frac{(8.9 \\times 10^8)}{(3.3 \\times 10^4)} written in scientific notation?<\/p>\n\n\n\n

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

The Correct Answer and Explanation is:<\/strong>1<\/a><\/sup><\/p>\n\n\n\n\n\n

Correct Answer:<\/strong> 3 x 10\u2074<\/p>\n\n\n\n

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

To find the best estimate for the expression \\frac{(8.9 \\times 10^8)}{(3.3 \\times 10^4)}, we can round the coefficients to the nearest whole numbers to simplify the calculation. This approach allows us to quickly approximate the answer.<\/p>\n\n\n\n

The original expression is:<\/p>\n\n\n\n

8.9\u00d71083.3\u00d71043.3\u00d71048.9\u00d7108\u200b<\/code><\/pre>\n\n\n\n
Step 1: Estimate the coefficients<\/strong>
First, round the decimal numbers (the coefficients) to the nearest integer to make the division easier.<\/p>\n\n\n\n
    \n
  • 8.9 is very close to 9.<\/li>\n\n\n\n
  • 3.3 is very close to 3.<\/li>\n<\/ul>\n\n\n\n
    Now, substitute these rounded numbers back into the expression:<\/p>\n\n\n\n
    \u22489\u00d71083\u00d7104\u22483\u00d71049\u00d7108\u200b<\/code><\/pre>\n\n\n\n
    Step 2: Divide the coefficients and the powers of 10 separately<\/strong>
    When dividing numbers in scientific notation, the process is broken into two parts: dividing the coefficients and dividing the powers of 10.<\/p>\n\n\n\n
      \n
    • Divide the coefficients:<\/strong>
      9\u00f73=39\u00f73=3<\/code><\/li>\n\n\n\n
    • Divide the powers of 10:<\/strong>
      To divide powers with the same base, we use the quotient rule of exponents, which states that\u00a0am\u00f7an=am\u2212na<\/em>m<\/em>\u00f7a<\/em>n<\/em>=a<\/em>m<\/em>\u2212n<\/em><\/code>. In this case, we subtract the exponent in the denominator from the exponent in the numerator.
      108\u00f7104=10(8\u22124)=104108\u00f7104=10(8\u22124)=104<\/code><\/li>\n<\/ul>\n\n\n\n
      Step 3: Combine the results<\/strong>
      Finally, combine the results from the two parts to get the estimated answer in scientific notation.
      The new coefficient is 3, and the new power of 10 is 10\u2074.<\/p>\n\n\n\n
      Therefore, the best estimate is:<\/p>\n\n\n\n
      3\u00d71043\u00d7104<\/code><\/pre>\n\n\n\n
      This result is already in proper scientific notation, as the coefficient (3) is a number between 1 and 10. Comparing this estimate with the given options, we find that 3 x 10\u2074 is one of the choices.<\/p>\n\n\n\n
      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"
      Which is the best estimate for \\frac{(8.9 \\times 10^8)}{(3.3 \\times 10^4)} written in scientific notation? The Correct Answer and Explanation is:1 Correct Answer: 3 x 10\u2074 Explanation: To find the best estimate for the expression \\frac{(8.9 \\times 10^8)}{(3.3 \\times 10^4)}, we can round the coefficients to the nearest whole numbers to simplify the calculation. This approach […]<\/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-232496","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232496","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=232496"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232496\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=232496"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=232496"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=232496"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}