{"id":228139,"date":"2025-06-07T03:45:42","date_gmt":"2025-06-07T03:45:42","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=228139"},"modified":"2025-06-07T03:45:44","modified_gmt":"2025-06-07T03:45:44","slug":"express-the-number-0-000216-in-scientific-notation-2-16-x-10-4","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/07\/express-the-number-0-000216-in-scientific-notation-2-16-x-10-4\/","title":{"rendered":"Express the number 0.000216 in scientific notation (2.16 x 10^-4)"},"content":{"rendered":"\n
Express the number 0.000216 in scientific notation (2.16 x 10^-4). Express 166,000 in exponential (scientific) notation (1.66 x 10^5). Express the number 8.64 x 10^-3 in common decimal form (0.00864). Express the number 1.16 x 10^4 in common decimal form (11600). How many significant figures are there in the number 0.045607007 (7)?<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
ChatGPT said:<\/h6>\n\n\n\n
Correct Answers:<\/h3>\n\n\n\n\n
0.000216 in scientific notation<\/strong>: \ud83d\udc49 2.16 \u00d7 10\u207b\u2074<\/strong><\/li>\n\n\n\n
166,000 in scientific notation<\/strong>: \ud83d\udc49 1.66 \u00d7 10\u2075<\/strong><\/li>\n\n\n\n
8.64 \u00d7 10\u207b\u00b3 in decimal form<\/strong>: \ud83d\udc49 0.00864<\/strong><\/li>\n\n\n\n
1.16 \u00d7 10\u2074 in decimal form<\/strong>: \ud83d\udc49 11,600<\/strong><\/li>\n\n\n\n
Significant figures in 0.045607007<\/strong>: \ud83d\udc49 7 significant figures<\/strong><\/li>\n<\/ol>\n\n\n\n\n\n\n\n
Explanation<\/h3>\n\n\n\n
Scientific notation<\/strong> is a way of expressing very large or very small numbers using powers of ten. It helps in simplifying calculations and presenting data clearly. A number in scientific notation is typically written as:a\u00d710na \\times 10^na\u00d710n<\/p>\n\n\n\n
where 1 \u2264 a < 10<\/strong>, and n<\/strong> is an integer.<\/p>\n\n\n\n
\n
For 0.000216<\/strong>, you move the decimal point 4 places to the right<\/strong> to get 2.16, so the exponent is \u20134<\/strong>. Hence, it’s written as 2.16 \u00d7 10\u207b\u2074<\/strong>.<\/li>\n\n\n\n
For 166,000<\/strong>, move the decimal point 5 places to the left<\/strong> to get 1.66. The exponent is +5<\/strong>, so it becomes 1.66 \u00d7 10\u2075<\/strong>.<\/li>\n<\/ul>\n\n\n\n
Converting scientific notation to decimal<\/strong> involves reversing the exponent:<\/p>\n\n\n\n
1.16 \u00d7 10\u2074<\/strong>: Move the decimal 4 places right<\/strong>, resulting in 11,600<\/strong>.<\/li>\n<\/ul>\n\n\n\n
Now, regarding significant figures<\/strong>, these are the digits in a number that carry meaningful information about its precision. The rules are:<\/p>\n\n\n\n\n
All non-zero digits<\/strong> are significant.<\/li>\n\n\n\n
Any zeros between non-zero digits<\/strong> are significant.<\/li>\n\n\n\n
Leading zeros<\/strong> (zeros before the first non-zero digit) are not<\/em> significant.<\/li>\n\n\n\n
Trailing zeros after a decimal point<\/strong> are<\/em> significant.<\/li>\n<\/ol>\n\n\n\n
In 0.045607007<\/strong>, we identify:<\/p>\n\n\n\n
\n
Ignore the leading zeros: \u20180.0\u2019<\/strong>.<\/li>\n\n\n\n
All these are either non-zero or meaningful zeros between or after significant digits.<\/li>\n<\/ul>\n\n\n\n
So, the number has 7 significant figures<\/strong>: 4, 5, 6, 0, 7, 0, 0, 7<\/strong> \u2192 7 meaningful digits.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"
Express the number 0.000216 in scientific notation (2.16 x 10^-4). Express 166,000 in exponential (scientific) notation (1.66 x 10^5). Express the number 8.64 x 10^-3 in common decimal form (0.00864). Express the number 1.16 x 10^4 in common decimal form (11600). How many significant figures are there in the number 0.045607007 (7)? The Correct Answer […]<\/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-228139","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228139","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=228139"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228139\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=228139"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=228139"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=228139"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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