Sun The Sun with a group of sunspots, as observed by the Solar Dynamics Observatory spacecraft, October 18, 2014. The Sun is so large that scientific notation is used to describe its qualities. For example, its mass is about 2 ⨉ 1033 grams (4 ⨉ 1030 pounds), or when written out, 2,000,000,000,000,000,000,000,000,000,000,000 grams (4,000,000,000,000,000,000,000,000,000,000 pounds). (more) scientific notation mathematics Actions Cite verifiedCite While every effort has been made to follow citation style rules, there may be some discrepancies. Please refer to the appropriate style manual or other sources if you have any questions. Select Citation Style MLA APA Chicago Manual of Style Copy Citation Share Share Share to social media Facebook X URL https://www.britannica.com/science/scientific-notation Give Feedback External Websites Feedback Corrections? Updates? Omissions? Let us know if you have suggestions to improve this article (requires login). Feedback Type Select a type (Required) Factual Correction Spelling/Grammar Correction Link Correction Additional Information Other Your Feedback Submit Feedback Thank you for your feedback Our editors will review what you’ve submitted and determine whether to revise the article.

　　External Websites University of Hawaii - Department of Physics - Powers of 10 and Scientific Notation IEER On-Line Classroom - Practice with Scientific Notation IEER On-Line Classroom - Scientific Notation Print Cite verifiedCite While every effort has been made to follow citation style rules, there may be some discrepancies. Please refer to the appropriate style manual or other sources if you have any questions. Select Citation Style MLA APA Chicago Manual of Style Copy Citation Share Share Share to social media Facebook X URL https://www.britannica.com/science/scientific-notation Feedback External Websites Feedback Corrections? Updates? Omissions? Let us know if you have suggestions to improve this article (requires login). Feedback Type Select a type (Required) Factual Correction Spelling/Grammar Correction Link Correction Additional Information Other Your Feedback Submit Feedback Thank you for your feedback Our editors will review what you’ve submitted and determine whether to revise the article.

　　External Websites University of Hawaii - Department of Physics - Powers of 10 and Scientific Notation IEER On-Line Classroom - Practice with Scientific Notation IEER On-Line Classroom - Scientific Notation Also known as: standard form Written by L. Sue Baugh L. Sue Baugh is a writer and editor who works in the educational, business, and science/medical fields. L. Sue Baugh Fact-checked by The Editors of Encyclopaedia Britannica Encyclopaedia Britannica's editors oversee subject areas in which they have extensive knowledge, whether from years of experience gained by working on that content or via study for an advanced degree. They write new content and verify and edit content received from contributors. The Editors of Encyclopaedia Britannica Last Updated: Sep 30, 2024 • Article History Table of Contents Also called: standard form (Show more) Ask the Chatbot a Question Ask the Chatbot a Question scientific notation, method of writing large or small numbers in a shorter form. For example, 4,800,000,000,000 is written in scientific notation as 4.8 ⨉ 1012. Similarly, 0.0000000000048 is written as 4.8 ⨉ 10-12. These numbers are referred to as “4.8 times 10 to the power of 12” and “4.8 times 10 to the power of negative 12,” respectively. Scientific notation is used in fields such as engineering, chemistry, microbiology, physics, and astronomy where very large and very small numbers are common.

　　The basic formula used to write numbers in scientific notation ism ⨉ 10n,where m is a number greater than or equal to 1 but less than 10, 10 is the base number, and n is the exponent, or power of ten, which is a positive or negative whole number. The number 10n is equal to 10 multiplied by itself n times. For example, 104 = 10 ⨉ 10 ⨉ 10 ⨉ 10 = 10,000.

　　To write a large number in scientific notation, one moves the decimal place to the left to form a number between 1 and 10. One then counts the number of places the decimal place was moved to the left. The base number 10 is raised to the power of the number of places the decimal was moved to the left. For example, if the number is 4,900,000,000, m = 4.9. The decimal place has been moved nine places to the left, so n = 9. The number 4,900,000,000 written in scientific notation is 4.9 ⨉ 109.

　　For small numbers, the procedure is much the same. One moves the decimal place to the right to form a number between 1 and 10. One then counts the number of places the decimal place was moved to the right. The base number 10 is raised to the power of the negative number of places the decimal was moved to the right. For example, if the number is 0.00000036, m = 3.6. The decimal place has been moved seven places to the right, so n = -7. The number 0.00000036 written in scientific notation is 3.6 ⨉ 10-7.

　　Scientific notation allows one to multiply, divide, add, and subtract very large or very small numbers more easily. For multiplication of two numbers m ⨉ 10n and a ⨉ 10b,(m ⨉ 10n) ⨉ (a ⨉ 10b)= (m ⨉ a) ⨉ 10n + b.Division works much the same:(m ⨉ 10n)/(a ⨉ 10b)= (m/a) ⨉ 10n - b.

　　For addition and subtraction using scientific notation, the exponents must always be the same power of ten. That is, (m ⨉ 10n) ± (c ⨉ 10n)= (m ± c) ⨉ 10n.When the exponents are different powers, one of them can be changed to match the other. For example,8.2 ⨉ 104 + 3.2 ⨉ 103= 8.2 ⨉ 104 + 0.32 ⨉ 104,since 3.2 = 0.32 ⨉ 101. Therefore, the solution is 8.52 ⨉ 104.