# per cent

The per cent may be in general interpreted to mean a ‘hundredth’. So e.g. 5 per cent is ‘5 hundredths’, i.e. $\frac{5}{100}$.

In practice, giving some number of per cents, one means so many hundredths of a quantity given in the same or being clear from the context; for example, we can say that the illiteracy in the world is about 20 per cent – meaning that 20/100 of the adults of the world cannot read. If we say that the interest (rate) of a loan is 8 per cent, it means that one must pay interest for the loan 8/100 of the amount of the loan in a year.

If a percentage of a quantity has changed e.g. from 12% to 15%, we must not say that it has grown 3% but that it has grown 3 percentage points.

Determination of percentage

How many percent a number $a$ is of a second number $b$? The answer, the per cent number $p$, is obtained from

$p={\displaystyle \frac{a}{b}}\cdot 100.$ | (1) |

The number $b$ here is called the base value and $a$ the per cent value(?). Essentially, the procedure in (1) may be replaced by converting the ratio $\frac{a}{b}$ to hundredths, which can be done formally by multiplying this ratio by $1=\frac{100}{100}=100\%$:

$$\frac{a}{b}=\frac{a}{b}\cdot 100\%.$$ |

Title | per cent |

Canonical name | PerCent |

Date of creation | 2013-03-22 17:32:43 |

Last modified on | 2013-03-22 17:32:43 |

Owner | CWoo (3771) |

Last modified by | CWoo (3771) |

Numerical id | 7 |

Author | CWoo (3771) |

Entry type | Definition |

Classification | msc 97D99 |

Classification | msc 00A69 |

Synonym | percent |

Defines | percentage point |

Defines | per cent number |

Defines | base value |

Defines | per cent value |