## Percentages, Fractions and Decimals

Percentages, fractions and decimals are essentially the same idea in different forms. A fraction is one whole number divided by another whole number eg.2 over 5, and so is a percentage, except that the denominator is always 100 eg. 40%=40 over 100. To change any fraction or percentage into a decimal we actually carry out the division, so40%=40 over 100 =0.4.

The table below shows some examples of this equivalence.

Fraction | Decimal | Percentage,% |

2 over 25 | 0.08 | 8 |

7 over 50 | 0.14 | 14 |

3 over 10 | 0.3=0.30 | 30 |

3 over 8 | 0.375 | 37.5 |

7 over 20 | 0.35 | 35 |

1 over 1 | 1 | 100 |

47 over 40 | 1.175 | 117.6 |

2=2 over 1 | 2 | 200 |

3 over 2 | 1.5 | 150 |

Several things can be noted about the numbers in the table:

A whole number is a fraction since we can write for example, 2 as 2 over 1.

A percentage greater than 100% is possible – the numerator is greater than the denominator.

Given a percentage we can find the fraction by writing the percentage over 100 and the decimal by carrying out the division.

Given a decimal we can find the percentage by writing the multiplying by 100.

Given a fraction we can find the decimal by carrying out the division and the percentage by multiplying by 100.