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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!
The United States national debt is close to $1.9795 x 1013.
There are approximately 3.24 x 108 people who currently live in the United States.
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
Example:
| (7.2 x 104) | x | (1.5 x 103) | |||||||
| (7.2 x 104) | x | (1.5 x 103) | = | (7.2 x 1.5) | x | (104 + 3) | |||
| 10.8 | x | 107 | ← | Move decimal. | |||||
| 1.08 | x | 108 |
Dividing numbers in scientific notation
Example:
| (3.5 x 109) | ÷ | (2.2 x 106) | |||||||
| (3.5 x 109) | ÷ | (2.2 x 106) | = | (3.5 ÷ 2.2) | x | (109 - 6) | |||
| 1.59 | x | 103 | ← | Already scientific notation. |
Watch Scientific Notation: Multiplication and Division, from Tyler Dewitt, to see examples of each type of problem:
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.
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:
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.
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