## Content description

Make connections between equivalent fractions, decimals and percentages (ACMNA131)

Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies (ACMNA132)

Source: Australian Curriculum, Assessment and Reporting Authority (ACARA)

## Percentage

Percentages are another way of expressing fractions with denominators that are ten, 100, 1000 and so on.

*Per centum* is Latin, meaning 'out of 100'. So 45 **per cent** or 45% means 45 out of 100 and we write it as a fraction: \(\dfrac{45}{100}\).

If we tallied the colours of 100 cars that passed a point on the highway and 50 were white, we could say that 50 out of 100 or \(\dfrac{50}{100}\) or \(\dfrac{1}{2}\) or 0.5 or 50% of those cars were white.

It is useful to know some common percentage conversions. For more about the connection between decimals, fractions and percentages see Connecting fractions, decimals and percentages.

### Percentage conversions

Fraction | Decimal | Percentage |
---|---|---|

\(\dfrac{1}{20}\) | 0.05 | 5% |

\(\dfrac{1}{10}\) | 0.1 | 10% |

\(\dfrac{1}{5}\) | 0.2 | 20% |

\(\dfrac{1}{4}\) | 0.25 | 25% |

\(\dfrac{1}{2}\) | 0.5 | 50% |

1 | 1 | 100% |

2\(\dfrac{1}{2}\) | 2.5 | 250% |

You might notice that a decimal with two digits after the decimal point converts easily to a percentage. For example:

\begin{align}0.25&=25\%\\\\0.85&=85\%\\\\ 0.99&=99\%\end{align}