How to Multiply and Divide in Scientific Notation? (+FREE Worksheet!)

Related Topics

• How to Round Decimals
• How to Multiply and Divide Decimals
• How to Add and Subtract Decimals
• How to Compare Decimals

Step by step guide to Multiply and Divide Scientific Notations

Multiplying numbers that are in the form of a scientific notation is relatively simple because multiplying by coefficients of ten is simple.

To multiply two numbers in scientific notation:

• Step 1: Multiply their coefficients which may be a decimal number or an integer.
• Step 2: Multiply the two exponential numbers (with a base of \(10\)) by adding their powers together.

To divide two numbers in scientific notation:

• Step 1: divide their coefficients which may be a decimal number or an integer.
•  Step 2: divide the two exponential numbers (with a base of \(10\)) by subtracting their powers from each other.

The answer must be converted to scientific notation.

Multiplication and Division in Scientific Notation – Example 1:

Write the answers in scientific notation. \((2.2\times 10^6) (4\times 10^{ \ -3})=\)

Solution:

First, multiply the coefficients: \(2.2\times 4=8.8\)

Add the powers of \(10\): \(10^6\times 10^{ \ -3}=10^{6+(-3)}= 10^ {6-3}= 10^3\)

Then: \((2.2\times 10^6) (4\times 10^{ \ -3})=8.8\times 10^3\)

Multiplication and Division in Scientific Notation – Example 2:

Write the answers in scientific notation. \(\frac{7.5\times 10^9}{1.5\times 10^5}\)

Solution:

First, divide the coefficients: \(\frac{7.5}{1.5}=5\)

Subtract the power of the exponent in the denominator from the exponent in the numerator: \(\frac{10^9}{10^5}=10^{9-5}=10^4\)

Then: \(\frac{7.5\times 10^9}{1.5\times 10^5}=5\times 10^4\)

Multiplication and Division in Scientific Notation – Example 3:

Write the answers in scientific notation. \((1.1\times 10^9) (9\times 10^{ \ -4})=\)

Solution:

First, multiply the coefficients: \(1.1\times 9=9.9\)

Add the powers of \(10\): \(10^9\times 10^{ \ -4}=10^ { 9+(-4)}=10^ {9-4} = 10^5\)

Then: \((1.1\times 10^9) (9\times 10^{ \ -4})=9.9\times 10^5\)

Multiplication and Division in Scientific Notation – Example 4:

Write the answers in scientific notation. \(\frac{4.5\times 10^{-7}}{5\times 10^2}\)

Solution:

First, divide the coefficients: \(\frac{4.5}{5}=0.9\)

Subtract the power of the exponent in the denominator from the exponent in the numerator: \(\frac{10^{-7}}{10^2}=10^{-7-2}=10^{-9}\)

Then: \(\frac{4.5\times 10^{-7}}{5\times 10^2}=0.9\times 10^{-9}\)

Now, convert the answer to scientific notation: \(0.9\times 10^{-9}=9\times 10^{-10}\)

Exercises for Multiplying and Dividing Scientific Notations

Write the answers in scientific notation. 

1. \(\color{blue}{(4.2\times 10^6) (3\times 10^{ \ -9})=}\)
2. \(\color{blue}{(5\times 10^8) (3.6\times 10^{ \ -6})=}\)
3. \(\color{blue}{(4.9\times 10^7) (2\times 10^{ \ -5})=}\)
4. \(\color{blue}{\frac{6.3\times 10^{-9}}{9\times 10^5}}\)
5. \(\color{blue}{\frac{8.8\times 10^9}{4\times 10^2}}\)
6. \(\color{blue}{\frac{9.6\times 10^{-5}}{3\times 10^4}}\)

1. \(\color{blue}{1.26\times 10^{-2}}\)
2. \(\color{blue}{1.8\times 10^3}\)
3. \(\color{blue}{9.8\times 10^2}\)
4. \(\color{blue}{7\times 10^{-15}}\)
5. \(\color{blue}{2.2\times 10^7}\)
6. \(\color{blue}{3.2\times 10^{-9}}\)