I have already discussed **clock arithmetic**, **modulo division**, and **number bases**. We further our discussion in this post by learning how to change numbers from one base to another.

The number system that we are using everyday is called the **decimal number system** or the base 10 number system (*deci* means 10). It is believed that this system was developed because we have 10 fingers.

In the base 10 system, the digits are composed of 0 up to 9. Adding 1 to 9, the largest digit in this system, will give us 10. That is, we replace 9 in the ones place with 0, and add 1 to the tens place which is the next larger place value.

Another way to write a number in base 10 is by multiplying its digits by powers of 10 and adding them. For example, the number 2578 can be rewritten in expanded form as