How To Multiply Numbers In Scientific Notation - WikiHow

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How to Multiply Numbers in Scientific Notation Download Article Explore this Article IN THIS ARTICLE 1 Multiply the coefficients. 2 Multiply the bases. 3 Multiply whole numbers by the new power of 10. 4 Convert the number to scientific notation if needed. + Show 1 more... - Show less... Other Sections Related Articles Expert Interview References Co-authored by JohnK Wright V and Hannah Madden

Last Updated: September 11, 2024 Fact Checked

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This article was co-authored by JohnK Wright V and by wikiHow staff writer, Hannah Madden. JohnK Wright V is a Certified Math Teacher at Bridge Builder Academy in Plano, Texas. With over 20 years of teaching experience, he is a Texas SBEC Certified 8-12 Mathematics Teacher. He has taught in six different schools and has taught pre-algebra, algebra 1, geometry, algebra 2, pre-calculus, statistics, math reasoning, and math models with applications. He was a Mathematics Major at Southeastern Louisiana and he has a Bachelor of Science from The University of the State of New York (now Excelsior University) and a Master of Science in Computer Information Systems from Boston University. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 25,681 times.

Learning about scientific notation and stuck on a multiplication problem? While these equations may look daunting at first, they’re actually pretty easy to calculate once you know the right steps to take. In this article, we’ll walk you through multiplying numbers in scientific notation and give you examples to follow along with, too.

Things You Should Know

• To multiply scientific notation, first multiply the coefficients, then use the rule of exponents to multiply the bases.
• If the new coefficient is less than 10, multiply the new number by the new power of 10 to get your solution.
• If the new coefficient is more than 10, convert it to scientific notation and multiply it by the new power of 10.[1]

Steps

1

Multiply the coefficients.

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1. Start by multiplying the whole numbers in the equation. When you multiply scientific notation, you can break things up into whole numbers vs powers of 10.[2] To get your new coefficient, simply multiply the whole numbers together.[3] For example:
   • Let’s say our problem is ( 2 × 10 4 ) × ( 6 × 10 7 ) {\displaystyle (2 \times 10^4) \times (6 \times 10^7)}
   • Our first step would be to multiply the coefficients: 2 × 6 = 12 {\displaystyle 2 \times 6 = 12}
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2

Multiply the bases.

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1. Use the rule of exponents to multiply the powers of 10. The rule of exponents tells us that when we multiply powers of 10, all we need to do is add the exponents together.[4] This will give us our base.[5]
   • To continue our example from above, multiplying the bases would look like this: 10 4 × 10 7 {\displaystyle 10^4 \times 10^7 }
   • Using the rule of exponents, we would convert the problem to 10 4 + 10 7 = 10 11 {\displaystyle 10^4 + 10^7 = 10^{11}} , because 4 + 7 = 11 {\displaystyle 4 + 7 = 11}

3

Multiply whole numbers by the new power of 10.

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1. If your new coefficient is a whole number, combine it with your new base. If you finish up your problem and there are no decimals to deal with, then you’re done! Simply multiply your whole number by the new power of 10 to get the answer.[6]
   • In our example above, our answer would be 12 × 10 11 {\displaystyle 12 \times 10^{11}}
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4

Convert the number to scientific notation if needed.

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1. If your coefficient is not in scientific notation, convert it to scientific notation. To do that, move the decimal point to the left, then count how many times it’s moved.[7] After that, multiply your new base by the base you solved for to get your answer.[8] For example:
   • ( 2.3 × 10 4 ) × ( 6.6 × 10 7 ) {\displaystyle (2.3 \times 10^4) \times (6.6 \times 10^7)}
   • ( 2.3 × 6.6 = 16.38 ) × ( 10 4 × 10 7 ) {\displaystyle (2.3 \times 6.6 = 16.38) \times (10^4 \times 10^7)}
   • 16.38 × 10 11 {\displaystyle 16.38 \times 10^{11}}
   • Since your coefficient is not in scientific notation (because it’s greater than 10), move the decimal point to the left and convert the problem to scientific notation:
     • 1.638 × 10 1 {\displaystyle 1.638 \times 10^1}
   • Now, multiply that base by the base we solved for earlier:
     • 10 1 × 10 11 {\displaystyle 10^1 \times 10^{11}}
     • The answer is 1.638 × 10 12 {\displaystyle 1.638 \times 10^{12}}

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Expert Interview

Thanks for reading our article! If you’d like to learn more about math, check out our in-depth interview with JohnK Wright V.

References

1. ↑ https://davenport.libguides.com/math-skills-overview/scientific-notation
2. ↑ JohnK Wright V. Texas Certified Math Teacher. Expert Interview
3. ↑ https://web.lemoyne.edu/giunta/chm151L/scinot.html
4. ↑ JohnK Wright V. Texas Certified Math Teacher. Expert Interview
5. ↑ https://flexbooks.ck12.org/cbook/ck-12-interactive-middle-school-math-8-for-ccss/section/9.8/primary/lesson/multiplying-dividing-numbers-in-scientific-notation-msm8-ccss/
6. ↑ https://janus.astro.umd.edu/astro/scinote/help.html
7. ↑ JohnK Wright V. Texas Certified Math Teacher. Expert Interview
8. ↑ https://web.lemoyne.edu/giunta/chm151L/scinot.html

About This Article

Co-authored by: JohnK Wright V Texas Certified Math Teacher This article was co-authored by JohnK Wright V and by wikiHow staff writer, Hannah Madden. JohnK Wright V is a Certified Math Teacher at Bridge Builder Academy in Plano, Texas. With over 20 years of teaching experience, he is a Texas SBEC Certified 8-12 Mathematics Teacher. He has taught in six different schools and has taught pre-algebra, algebra 1, geometry, algebra 2, pre-calculus, statistics, math reasoning, and math models with applications. He was a Mathematics Major at Southeastern Louisiana and he has a Bachelor of Science from The University of the State of New York (now Excelsior University) and a Master of Science in Computer Information Systems from Boston University. This article has been viewed 25,681 times. 9 votes - 91% Co-authors: 6 Updated: September 11, 2024 Views: 25,681 Categories: Science

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Yes No Advertisement Cookies make wikiHow better. By continuing to use our site, you agree to our cookie policy. Co-authored by: JohnK Wright V Texas Certified Math Teacher Co-authors: 6 Updated: September 11, 2024 Views: 25,681 91% of readers found this article helpful. 9 votes - 91% Click a star to add your vote

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