### LESSON: Operations with Exponential Numbers

#### Adding and Subtracting with Scientific Notation

#### Multiplying and Dividing with Scientific Notation

#### Example Problem

**Operations with Exponential Numbers**

In order to add or subtract exponential numbers, the exponents must be the same. If the exponents are not the same, one of the numbers must be changed so that the exponents are the same. Once the exponents are the same, the numbers are added and the same exponents are carried.

**Example: ** Add 5.0 × 10^{5} and 4.0 × 10^{4}.

**Solution: ** In order to add these numbers, we can change 4.0 × 10^{4} to 0.40 × 10^{5} and then add 0.40 × 10^{5} to 5.0 × 10^{5} which yields 5.4 × 10^{5}.

When you multiply exponential numbers, the numbers multiply and the exponents add.

**Example:** Multiply 5.0 × 10^{5} and 4.0 × 10^{4}.

**Solution:**

**Example:** Multiply 6.0 × 10^{3} and 2.0 × 10^{-5}.

**Solution: **

When you divide exponential numbers, the numbers are divided and the exponent of the divisor is subtracted from the exponent of the dividend.

**Example:** Divide 6.0 × 10^{3} by 2.0 × 10^{-5}.

**Solution:**

**After you have completed this part of the lesson, you can check the associated box on the main course page to mark it as complete **