# Decimal

The term decimal indicates a base of ten. The numeral system we use most of the time is called the decimal numeral system because it is based on groupings of ten. "Decimal" is also used as another name for a decimal fraction and decimal mixed number.

### What exactly is a decimal?

There are many different numeral systems in use today, but the most common is the decimal numeral system. It is a way of writing numbers such that the position of the number indicates the power of 10 that the digit occupying the position is multiplied by; the power of 10 attached to a specific position is referred to as the place value. Refer to the figure below.

To really understand the decimal numeral system, lets break down the number 5613.2297. What this really represents is:

(103) × 5 + (102) × 6 + (101) × 1 + (100) × 3 + (10-1) × 2 + (10-2) × 2 + (10-3) × 9 + (10-4) × 7

Note that the digits before the decimal point are powers of 10 (10n), while those after the decimal point are reciprocals of powers of 10 ( ). Also, the further left a number is in the decimal numeral system, the larger its magnitude.

If we further expand the expression above, we get:

5000 + 600 + 10 + 3 + 0.2 + 0.02 + 0.009 + 0.0007 = 5613.2297

As we can see, the decimal numeral system allows us to express numbers much more efficiently. In the case of the decimal numeral system, the base is 10, but there are also other positional numeral systems that use a different base, such as the hexadecimal numeral system, which uses a base of 16, and the binary numeral system, which uses a base of 2.

See also decimal fraction, decimal mixed number, decimal numeration system.