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*Contributor: Briana Pincherri. Lesson ID: 11678*

How do you multiply and divide monstrous numbers, like the national debt and how often you've been told to clean your room? Scientific notation sounds scary, but it's easy if you follow this lesson!

categories

subject

Math

learning style

Visual

personality style

Lion, Otter

Grade Level

Middle School (6-8)

Lesson Type

Quick Query

The United States national debt is close to $1.9795 x 10^{13}.

There are approximately 3.24 x 10^{8} people who currently live in the United States.

- If you divided the national debt equally amongst each person, how much would each individual owe?

When you are dealing with very large numbers, *scientific notation* comes in quite handy.

Hopefully, at this point, you are familiar with writing numbers in scientific notation and standard form. If you are not, please complete the Elephango lesson found under **Additional Resources** in the right-hand sidebar.

If you have those skills mastered, this lesson is a great place to build on the scientific notation skills you already possess. This lesson is all about multiplying and dividing numbers in scientific notation.

Let's take a look at just how to do each!

**Multiplying numbers in scientific notation**

- Re-write the problem, separating the decimals and the base and exponents.

- Multiply the decimal numbers together, then multiply the bases and exponents together. (Use exponent rules to add the exponents and keep the base 10.)

- Change the answer to scientific notation. (Move numbers so one digit is before decimal and adjust the exponent.)

Example:

(7.2 x 10^{4}) |
x | (1.5 x 10^{3}) |
|||||||

(7.2 x 10^{4}) |
x | (1.5 x 10^{3}) |
= | (7.2 x 1.5) | x | (10^{4 + 3}) |
|||

10.8 | x | 10^{7} |
← | Move decimal. | |||||

1.08 | x | 10^{8} |

**Dividing numbers in scientific notation**

- Re-write the problem, separating the decimals and the base and exponents.

- Divide the decimal numbers. Then, divide the bases and exponents (by subtracting the exponents and keeping the base 10).

- If needed, change the answer to scientific notation. (Move numbers so just one digit is before the decimal and adjust the exponent.)

Example:

(3.5 x 10^{9}) |
÷ | (2.2 x 10^{6}) |
|||||||

(3.5 x 10^{9}) |
÷ | (2.2 x 10^{6}) |
= | (3.5 ÷ 2.2) | x | (10^{9 - 6}) |
|||

1.59 | x | 10^{3} |
← | Already scientific notation. |

Watch *Scientific Notation: Multiplication and Division*, from Tyler Dewitt, to see examples of each type of problem:

- What sticks out to you from the video?

Both operations are similar, in that you combine the decimal numbers together, and the bases and exponents together.

The main thing that tends to be forgotten is that *you must make sure your answer is in scientific notation*.

- What does this mean?

It means you MUST check to make sure that your answer has one digit before the decimal point. If it doesn't (it may have more than one or none), you must adjust the final answer using the rules of scientific notation.

As quick a review, here they are:

- When moving a decimal LEFT, adjust your exponent by adding 1.

- When moving a decimal RIGHT, adjust your exponent by subtracting 1.

Let's put all of this information to practice. Head to the *Got It?* section to see just how well you are doing with these new concepts.