# Decimal Expansion

A decimal is any number in our base-ten number system. A decimal point is used to separate the units place from the tenth place in the decimal. A decimal point is also used in currency to separate the dollars from the coins. For example if i said a certain pen costs \(1.30$\), what we mean by that is that the pen costs 1 dollar and 30 cents.

The diagram above shows how a decimal number is written and that each digit has its own unique identification. This identification is known as place value. As we move from the decimal point towards the left and right the place value gets 10 times bigger or smaller respectively. In the above decimal number \(8\) is said to be found in the **TENTHS or \(\frac{1}{10}th\)** place, and as we move one step towards the right. the number \(9\) is found in the, **HUNDREDTH or \(\frac{1}{100}th\)** position.

Decimal numbers are used when a whole number doesn't give enough information. Think of a decimal number as the sum of a whole number and a certain fraction. For example if i said i have three and a three-tenth of an apple. It can be written as \(3+\frac{3}{10}\) but that can be a lot of writing and a swifter and more simple way of writing it is since three-tenth is found in the tenth position \(3+\frac{3}{10}=3.3\) . We can see that the numbers found to the right of the decimal point are just a fraction of a unit. If we said twenty-four and , one-fifth, the decimal representation will be \(20+4+\frac{1}{5}\). We know that a fraction of a number is written after the decimal point and one-fifth of a number is equivalent to two-tenth of a number so we have \(24+\frac{2}{10}=24.2\).

**Cite as:**Decimal Expansion.

*Brilliant.org*. Retrieved from https://brilliant.org/wiki/decimal-numbers-base-10/