In terms of mathematics, a percentage is defined as a ratio, which has been expressed as a fraction of 100. The sign commonly used for expressing percentage is “%”, known as percentage sign. Percentage is also expressed using the abbreviation “pct.” or ”pc”. Percentage is a dimensionless pure number.

Basically, a fraction out of 100 is known as percentage. Percentage got its name from the Latin word “per centum”, where centum means 100 meaning “per 100”. Changing a percentage to a decimal is really easy and straight-forward method. But for people who have lost the practice may be prone to making errors especially if the percentage comes with decimals or if the percentage value is less than 10.

Example – 0.5% percentage means 0.005 or \(\frac{0.5}{100}\), which is less than 1%.

For converting a fraction to a percentage, place the numbers to be converted over 100. To reverse the process, that is, to convert percents to fractions, remove the sign of percent and then place a decimal point two places to the left.

## Percent Conversions

\(48\% = \frac{48}{100} = 0.48\)Convert 0.863 into percent

\(0.863 = 0.863 \times 100 \% = 86.3\%\)Convert \(\frac{3}{5}\) into decimal

\(\frac{3 \times 20}{5 \times 20} = \frac{60}{100} = 60 \%\)Since, you know that % means out of 100, so 300% mean \(\frac{300}{100}\) which is thrice of 100. In general, anything more than 100% of the number will be greater than the number

## Properties of Percents

Percentage is not cumulative in nature: for example if you start with Rs.100 and then decrease it by 20%, again decrease it by 20%, the result you will get won’t be Rs 60. If you do the proper math, the result you will get is:

Step1. Rs. 100 – Rs 20 = Rs 80

Step2. 20% of Rs 80= Rs. 16

So final result will be, Rs. 80 – Rs. 16 = Rs. 64.

Multiple percentages are not additive in nature: It is an important tip to remember and can come handy on the D-day. If a question asks for several percent changes in a row, then don’t add it as a simple multiplication, SOLVE IT.

Cheat Sheet for Percentage

Fraction |
Percentage value |

1 | 100% |

\(\frac{1}{2}\) |
50% |

\(\frac{1}{3}\) | 33.3% |

\(\frac{1}{4}\) | 25% |

\(\frac{1}{5}\) |
20% |

\(\frac{1}{6}\) | 16.67% |

\(\frac{1}{7}\) |
14.28% |

\(\frac{1}{8}\) |
12.5% |

\(\frac{1}{9}\) | 11.11% |

\(\frac{1}{10}\) | 10 10% |

\(\frac{1}{11}\) | 9.09% |

\(\frac{1}{12}\) | 8.33% |

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