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. $\color{blue}{3.2\times 10^{-9}}$