# 1.4 Decimals

Quantities can be smaller than one (such as 0.5 kg) or take values between whole numbers (such as a height of 1.65 metres). Numbers smaller than one are expressed as decimals or as fractions. Decimals are often easier to work with (especially when using a calculator). Decimals are explained in this section, and fractions following that (Section 1.7).

Decimals can be indicated on the number line in between whole numbers. 0.5 and 1.65 are indicated on the figure below.

Decimals arise when whole numbers are divided by ten, a hundred etc.

## Example 3

What is 3579 cents in dollars? (There are 100 cents in a dollar ($).)

### Answer

You need to divide 3579 by 100. To multiply a number by 100, you shift the digits two places to the left (and add zeros to fill the spaces). To reverse the process, i.e. to divide by 100, move the digits two places to the right. To show this, you need to mark the end of the units column, and this is done by means of a **decimal point**.

Th | H | T | U | |||||

3 | 5 | 7 | 9 | |||||

= | 3 | 5 | 7 | 9 | ||||

Digits moved two places to the right |

So the answer is 35.79, or in words, thirty five **point** seven nine (*not* seventy nine).

So 3579 cents = $35.79.