# How to Multiply and Divide in Scientific Notation

This article teaches you how to Multiply and Divide Scientific Notations into a few simple steps.

## 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 $$10$$: $$10^6\times 10^{ \ -3}=10^3$$

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 $$10$$: $$10^9\times 10^{ \ -4}=10^5$$

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

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