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What is a Base Number?

Instructor: Jessica Mommens

Jessie has taught elementary school for nine years and have a masters in Elementary Administration.

What are base numbers and how do we use them in math? The fact is that we deal with base numbers all the time when doing math and we don't even realize we are doing it. Read on to figure out what base numbers are and how we use them.

Definition

Base numbers are the number of units, or numbers, we use in our counting system, also called a number system. The most common base number is ten because the digits 0-9 are used in the number system. In other words, whenever we want to tell a number to someone we don't use any numbers besides 0-9. If it was a base-5 number system we would only use five different digits, like 0-4.

We can think of base numbers like the basement of a house, it is the 'foundation' of all of our math work. In this picture, the gray is the foundation of the house. It holds up the house and helps it do its job of keeping people safe. Base-10 numbers are the foundation of our math. It makes all math work!


Just like this house with a gray foundation, the numbers 0-9 work as our foundation to make our math function in base-10
picture of house and foundation


In math, a base number is written as a large number with a small 'floating' number up to the right of the base number. The base number is the large number before the floating number. The small 'floating' number is called the exponent. The exponent tells us how many times we should multiply our base number times itself.

Example

An example of how you may see this in math is as follows:

8 2

In this case 8 is the base number. To solve this, you would take the base number and multiply it by the number of times indicated by the exponent. In other words, you would multiply 8 times itself two times, or 8 x 8, which gives you 64. Therefore 8 2 is 64.

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