### Numbers: Ratios

### Fractions, decimals, percentages, and ratios

We have *seen **fractions*, *decimals*, *percentages*, and *ratios*. These are all ways to write the same number.

The relationship between fractions, decimal numbers, percentages and ratios

We can convert fractions, decimals, percentages, and ratios to one another.

For example, the fraction #\tfrac{1}{4}# is equal to the fraction #\tfrac{25}{100}#. This means that #\tfrac{1}{4}=25\%#. As a decimal number, this is #0.25#. The ratio is #1 : 4#.

We now see that fractions, decimals, percentages, and ratios are different ways to write the same thing.

We can use a combination of these different notations to perform calculations.

**Example**

\[\begin{array}{ccccc} &\text{fraction: }&&\dfrac{2}{5}& \\ \\ &\text{decimal: }&&0.4 &\\ \\ &\text{percentage: }&&40\%& \\ \\ &\text{ratio: }&&2:5 &\end{array}\]

#54\%=# #0.54#

We convert a percentage to a decimal number by dividing by #100#. When dividing by #100#, the decimal point moves two places to the left.

Therefore, #54\%=\frac{54}{100}=54:100=0.54#.

We convert a percentage to a decimal number by dividing by #100#. When dividing by #100#, the decimal point moves two places to the left.

Therefore, #54\%=\frac{54}{100}=54:100=0.54#.

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