## 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.2/5, and so is a percentage, except that the denominator is always 100 eg. 40%=40/100. To change any fraction or percentage into a decimal we actually carry out the division, so40%=40/100 =0.4.

The table below shows some examples of this equivalence.

Fraction | Decimal | Percentage,% |

2/25 | 0.08 | 8 |

7/50 | 0.14 | 14 |

3/10 | 0.3=0.30 | 30 |

3/8 | 0.375 | 37.5 |

7/20 | 0.35 | 35 |

1/1 | 1 | 100 |

47/40 | 1.175 | 117.6 |

2=2/1 | 2 | 200 |

3/2 | 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 2/1.

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/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.