{"id":198733,"date":"2025-03-10T09:49:38","date_gmt":"2025-03-10T09:49:38","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=198733"},"modified":"2025-03-10T09:49:40","modified_gmt":"2025-03-10T09:49:40","slug":"write-this-in-scientific-notation-with-one-digit-before-the-decimal-place-0-005030","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/10\/write-this-in-scientific-notation-with-one-digit-before-the-decimal-place-0-005030\/","title":{"rendered":"write this in scientific notation with one digit before the decimal place 0.005030"},"content":{"rendered":"\n<p>write this in scientific notation with one digit before the decimal place 0.005030 , 0.004502<\/p>\n\n\n\n<p>express the answer with correct number of significant figures assume that number represent measurements<\/p>\n\n\n\n<p>1) (34.7 X 4.26x 10-3 X 55.97) \/ ( 0.020 X 16.3x 104 )<\/p>\n\n\n\n<p>2) (4.5 X 350 X 3.832) \/ ( 5 x 47.3 )<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To express the numbers 0.005030 and 0.004502 in scientific notation with one digit before the decimal place:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>0.005030<\/strong>: Move the decimal point three places to the right to get 5.030, which corresponds to multiplying by 10\u00b3. Therefore, 0.005030 = 5.030 \u00d7 10\u207b\u00b3. This number has four significant figures: 5, 0, 3, and 0.<\/li>\n\n\n\n<li><strong>0.004502<\/strong>: Similarly, move the decimal point three places to the right to get 4.502, corresponding to multiplying by 10\u00b3. Thus, 0.004502 = 4.502 \u00d7 10\u207b\u00b3. This number also has four significant figures: 4, 5, 0, and 2.<\/li>\n<\/ul>\n\n\n\n<p><strong>Calculations:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Numerator<\/strong>: 34.7 \u00d7 4.26 \u00d7 10\u207b\u00b3 \u00d7 55.97 = 8,292.78018 \u00d7 10\u207b\u00b3 = 8.29278018<\/li>\n\n\n\n<li><strong>Denominator<\/strong>: 0.020 \u00d7 16.3 \u00d7 10\u2074 = 32600 \u00d7 10\u207b\u00b2 = 326.0 Therefore, the result is approximately 0.0025379132944785276. Considering significant figures:<\/li>\n\n\n\n<li>The numerator has three significant figures (34.7), three significant figures (4.26 \u00d7 10\u207b\u00b3), and four significant figures (55.97). The limiting factor is three significant figures.<\/li>\n\n\n\n<li>The denominator has two significant figures (0.020) and three significant figures (16.3 \u00d7 10\u2074), so the limiting factor is two significant figures. The result should be expressed with two significant figures: 0.0025.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\ue200calculator\ue202turn0calculator1\ue201<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Numerator<\/strong>: 4.5 \u00d7 350 \u00d7 3.832 = 6,037.8<\/li>\n\n\n\n<li><strong>Denominator<\/strong>: 5 \u00d7 47.3 = 236.5 Therefore, the result is approximately 25.51966173361522. Considering significant figures:<\/li>\n\n\n\n<li>The numerator has two significant figures (4.5), two significant figures (350), and four significant figures (3.832). The limiting factor is two significant figures.<\/li>\n\n\n\n<li>The denominator has one significant figure (5) and three significant figures (47.3), so the limiting factor is one significant figure. The result should be expressed with one significant figure: 30.<\/li>\n<\/ul>\n\n\n\n<p><strong>Explanation:<\/strong><\/p>\n\n\n\n<p><em>Scientific Notation:<\/em> This is a method of writing numbers that accommodates values too large or small to be conveniently written in standard decimal form. It expresses numbers as a product of two factors: a coefficient (a number between 1 and 10) and a power of ten. For example, 0.005030 can be written as 5.030 \u00d7 10\u207b\u00b3.<\/p>\n\n\n\n<p><em>Significant Figures:<\/em> These are the digits in a number that carry meaningful information about its precision. The rules for determining significant figures include:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>All non-zero digits are significant.<\/li>\n\n\n\n<li>Any zeros between significant digits are significant.<\/li>\n\n\n\n<li>Leading zeros (zeros before non-zero digits) are not significant.<\/li>\n\n\n\n<li>Trailing zeros in a number with a decimal point are significant.<\/li>\n<\/ul>\n\n\n\n<p>In calculations:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For multiplication and division, the result should have the same number of significant figures as the factor with the fewest significant figures.<\/li>\n\n\n\n<li>For addition and subtraction, the result should be rounded to the least precise decimal place.<\/li>\n<\/ul>\n\n\n\n<p><em>Application to Calculations:<\/em><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>In the first calculation, the numerator&#8217;s factors have 3, 3, and 4 significant figures, respectively, so the numerator is limited to 3 significant figures. The denominator&#8217;s factors have 2 and 3 significant figures, so the denominator is limited to 2 significant figures. Therefore, the final result should be rounded to 2 significant figures.<\/li>\n\n\n\n<li>In the second calculation, the numerator&#8217;s factors have 2, 2, and 4 significant figures, respectively, so the numerator is limited to 2 significant figures. The denominator&#8217;s factors have 1 and 3 significant figures, so the denominator is limited to 1 significant figure. Therefore, the final result should be rounded to 1 significant figure.<\/li>\n<\/ol>\n\n\n\n<p>Understanding and applying the rules of significant figures and scientific notation ensures precision and clarity in scientific measurements and calculations.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>write this in scientific notation with one digit before the decimal place 0.005030 , 0.004502 express the answer with correct number of significant figures assume that number represent measurements 1) (34.7 X 4.26x 10-3 X 55.97) \/ ( 0.020 X 16.3x 104 ) 2) (4.5 X 350 X 3.832) \/ ( 5 x 47.3 ) [&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 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-198733","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/198733","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=198733"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/198733\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=198733"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=198733"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=198733"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}