{"id":235298,"date":"2025-06-15T05:01:59","date_gmt":"2025-06-15T05:01:59","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=235298"},"modified":"2025-06-15T05:02:06","modified_gmt":"2025-06-15T05:02:06","slug":"change-each-of-the-following-to-scientific-notation-1-0-000147-1-47-x-10-4-2-0-543-5-43-x-10-1-3-648-6-48-x-102-4-3-0-x","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/15\/change-each-of-the-following-to-scientific-notation-1-0-000147-1-47-x-10-4-2-0-543-5-43-x-10-1-3-648-6-48-x-102-4-3-0-x\/","title":{"rendered":"Change each of the following to scientific notation: 1. 0.000147 = 1.47 x 10^-4 2. 0.543 = 5.43 x 10^-1 3. 648 = 6.48 x 10^2 4. 3.0 x"},"content":{"rendered":"\n
Change each of the following to scientific notation: 1. 0.000147 = 1.47 x 10^-4 2. 0.543 = 5.43 x 10^-1 3. 648 = 6.48 x 10^2 4. 3.0 x 10^-3 5. 7.1 x 10^64 6. 833 = 8.33 x 10^2 7. 7530 = 7.53 x 10^3 8. 9.2 x 10^4 9. 71,200 = 7.12 x 10^4 10. 0.014 x 10^2 Change each of the following from scientific notation to standard decimal notation: 1. 1.76 x 10^2 2. 4.27 x 10^-3 3. 9.85 x 10^-6 4. 3.49 x 10^14 5. 5.52 x 10^3 6. 2.17 x 10^1 7. 7.88 x 10^2 8. 1.35 x 10^-5 Determine the number of significant digits in each of the following: 1. 0.12090 mm = 5 significant digits 2. 0.0067 g = 2 significant digits 3. 2500 m = 4 significant digits 4. 43.07 cm = 4 significant digits 5. 26.509 cm = 5 significant digits 6. 0.20010 g = 5 significant digits Round each of the following to 3 significant figures: 1. 707.5 = 708 2. 2,300.2 = 2,300 3. 0.0003350 = 0.000335 4. 10.26730 = 10.3 Carry out the following operations to the proper number of significant figures: 1. 221.45 + 56.1 = 277.6 2. 89.001 \/ 25 = 3.56 3. 12.5 * 4000 = 50,000 5. (23.456 + 87.1) * (78.44 – 21.3) = 8,000.8<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
Corrected Answers and Explanation<\/h3>\n\n\n\n
Part 1: Convert to Scientific Notation<\/h4>\n\n\n\n\n
3.0 x 10^-3<\/strong> \u2014 Already in scientific notation<\/li>\n\n\n\n
7.1 x 10^64<\/strong> \u2014 Already in scientific notation<\/li>\n\n\n\n
0.014 x 10^2<\/strong> = 1.4<\/strong> (standard form) = 1.4 x 10^0<\/strong><\/li>\n<\/ol>\n\n\n\n
Part 2: Convert to Decimal Notation<\/h4>\n\n\n\n\n
1.76 x 10\u00b2<\/strong> = 176<\/strong><\/li>\n\n\n\n
4.27 x 10\u207b\u00b3<\/strong> = 0.00427<\/strong><\/li>\n\n\n\n
9.85 x 10\u207b\u2076<\/strong> = 0.00000985<\/strong><\/li>\n\n\n\n
3.49 x 10\u00b9\u2074<\/strong> = 349,000,000,000,000<\/strong><\/li>\n\n\n\n
5.52 x 10\u00b3<\/strong> = 5,520<\/strong><\/li>\n\n\n\n
2.17 x 10\u00b9<\/strong> = 21.7<\/strong><\/li>\n\n\n\n
7.88 x 10\u00b2<\/strong> = 788<\/strong><\/li>\n\n\n\n
1.35 x 10\u207b\u2075<\/strong> = 0.0000135<\/strong><\/li>\n<\/ol>\n\n\n\n
Part 3: Number of Significant Digits<\/h4>\n\n\n\n\n
2500 m<\/strong> = 2 significant digits<\/strong> (unless written as 2.500 x 10\u00b3)<\/li>\n<\/ol>\n\n\n\n
Part 4: Round to 3 Significant Figures<\/h4>\n\n\n\n\n
10.26730<\/strong> \u2192 10.3<\/strong> is incorrect. Correct rounding: 10.3<\/strong> (this is acceptable if interpreting only 3 significant digits<\/strong>). However, more accurate<\/strong> rounding of 10.26730 \u2192 10.3<\/strong> is valid due to the third digit rule.<\/li>\n<\/ol>\n\n\n\n
Part 5: Operations with Significant Figures<\/h4>\n\n\n\n\n
221.45 + 56.1<\/strong> = 277.6<\/strong>\n
\n
Round to 1 decimal place<\/strong>, the least precise (from 56.1).<\/li>\n<\/ul>\n<\/li>\n\n\n\n
89.001 \/ 25<\/strong> = 3.56<\/strong>\n
\n
89.001 has 5 sig figs, 25 has 2 \u2192 answer rounded to 2 sig figs.<\/li>\n\n\n\n
Final multiplication: 110.6 \u00d7 57.1 = 6311.26<\/strong> \u2192 3 sig figs \u2192 6.31 x 10\u00b3<\/strong> or 6310<\/strong><\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n\n\n\n\n
Explanation<\/h3>\n\n\n\n
Scientific notation expresses numbers as a product of a coefficient (between 1 and 10) and a power of ten. Small numbers are written with negative exponents; large numbers with positive ones. For instance, 0.000147 becomes 1.47 \u00d7 10\u207b\u2074, indicating that the decimal moves four places to the right.<\/p>\n\n\n\n
In reverse conversion, the exponent guides the placement of the decimal point. A positive exponent moves it to the right, while a negative one moves it to the left. For example, 4.27 \u00d7 10\u207b\u00b3 becomes 0.00427.<\/p>\n\n\n\n
Significant digits reflect precision. Non-zero digits are always significant. Zeros between digits or after a decimal point and a digit are also significant. For example, 0.12090 has five significant digits. Leading zeros never count, so 0.0067 has only two.<\/p>\n\n\n\n
When rounding to a specific number of significant figures, start from the leftmost non-zero digit and round based on the following digit. For example, 0.0003350 becomes 0.000335 when rounded to three significant figures.<\/p>\n\n\n\n
In arithmetic, different rules apply for precision. In addition and subtraction, the result must match the least number of decimal places. In multiplication and division, the result must reflect the operand with the fewest significant digits. For instance, 89.001 \u00f7 25 becomes 3.6 due to 25 having two significant digits.<\/p>\n\n\n\n
Expressions with multiple operations require applying rounding rules in stages. For example, in (23.456 + 87.1) \u00d7 (78.44 \u2013 21.3), rounding occurs after addition and subtraction before multiplying. Precision is preserved throughout using the least accurate step as the limiting factor.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"
Change each of the following to scientific notation: 1. 0.000147 = 1.47 x 10^-4 2. 0.543 = 5.43 x 10^-1 3. 648 = 6.48 x 10^2 4. 3.0 x 10^-3 5. 7.1 x 10^64 6. 833 = 8.33 x 10^2 7. 7530 = 7.53 x 10^3 8. 9.2 x 10^4 9. 71,200 = 7.12 x […]<\/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-235298","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/235298","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=235298"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/235298\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=235298"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=235298"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=235298"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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