Operations with Numbers in Scientific Notation – Practice Problems

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When dealing with numbers that are either very large or extremely small, knowing how to rewrite, and perform operations with, numbers in scientific notation can make handling such large or small numbers so much easier. The associative property and operations on exponents especially help when performing operations with numbers in scientific notation.

When multiplying numbers in scientific notation, like (a∙10^m)∙(b∙10^n), we can use the associative property to rewrite our multiplication, like (a∙b)∙(10^m∙10^n). The product (a∙b) is the product of two integers, and the product (10^m∙10^n), since they have the same base 10, will just follow the product property of exponents: (10^m∙10^n) = 10^(m+n). If the product c = (a∙b) is NOT greater than or equal to 1 and less than 10, then the answer c∙10^(m+n) must be rewritten in scientific notation by moving the decimal point of c in the appropriate direction and adding or subtracting the appropriate amount from the exponent of 10^(m+n).

When dividing numbers in scientific notation, like (a∙10^m)÷(b∙10^n), we will also use the associative property to rewrite our operation, like (a÷b)∙(10^m÷10^n), where (10^m÷10^n) can be further simplified using the quotient property of exponents: (10^m÷10^n) = 10^(m-n). So we will then have (a÷b)∙(10^m÷10^n)=(a÷b)∙(10^(m-n)). Again, we must have that (a÷b) is greater than or equal to 1, and less than 10.

Having the ability to perform operation with numbers in scientific notation will be like having a superpower in any scientific situation. Whether is is making calculations on Mars, measuring the effects of earthquakes, or just being in a lab, looking through a microscope.

Work with radicals and integer exponents.

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Exercises in this Practice Problem
Calculate the fox population of Mr. and Mrs. Fox's village.
Find the fox density of the town.
Determine the fox population in Norway.
Examine the different population densities.
Decide which numbers are written in scientific notation.
Complete the following operations using scientific notation.