Multiply and Divide Numbers in Scientific Notation
Learning Objectives
Multiply and divide numbers expressed in scientific notation
Multiplying and Dividing Numbers Expressed in Scientific Notation
Numbers that are written in scientific notation can be multiplied and divided rather simply by taking advantage of the properties of numbers and the rules of exponents that you may recall. To multiply numbers in scientific notation, first multiply the numbers that aren’t powers of 10 (the a in [latex]a\times10^{n}[/latex]). Then multiply the powers of ten by adding the exponents.
This will produce a new number times a different power of 10. All you have to do is check to make sure this new value is in scientific notation. If it isn’t, you convert it.
In the following video you will see an example of how to multiply tow numbers that are written in scientific notation.
In order to divide numbers in scientific notation, you once again apply the properties of numbers and the rules of exponents. You begin by dividing the numbers that aren’t powers of 10 (the a in [latex]a\times10^{n}[/latex]. Then you divide the powers of ten by subtracting the exponents.
This will produce a new number times a different power of 10. If it isn’t already in scientific notation, you convert it, and then you’re done.
Notice that when you divide exponential terms, you subtract the exponent in the denominator from the exponent in the numerator. You will see another example of dividing numbers written in scientific notation in the following video.
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CC licensed content, Original
Revision and Adaptation. Provided by: Lumen Learning. License: CC BY: Attribution
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Unit 11: Exponents and Polynomials, from Developmental Math: An Open Program. Provided by: Monterey Institute of Technology and Education. Located at: http://nrocnetwork.org/dm-opentext. License: CC BY: Attribution
Examples: Dividing Numbers Written in Scientific Notation. Authored by: James Sousa (Mathispower4u.com) for Lumen Learning. Located at: https://youtu.be/RlZck2W5pO4. License: CC BY: Attribution
Examples: Multiplying Numbers Written in Scientific Notation. Authored by: James Sousa (Mathispower4u.com) for Lumen Learning. Located at: https://youtu.be/5ZAY4OCkp7U. License: CC BY: Attribution