# Rounding

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**Rounding** can be challenging. Especially if the decimal you have to remove is a five, or the decimals you are up to remove are near *498…* or *502…*, or – even worse – *5001…*. Keep strong! There are simple rules for it. If not stated otherwise, we use commercial rounding (or *rounding half away from zero*) in this wiki, trailing decimals 0,…,4 are rounded towards zero, 5,…,9 are rounded away from zero.

Fourtunately, cent values of just intervals (except 1/1 and 2/1) are irrational.

## Example

Decimals | Result |
---|---|

20 | 701.9550008653874177445 |

19 | 701.955000865387417744 |

18 | 701.95500086538741774 |

17 | 701.9550008653874177 |

16 | 701.955000865387418 |

15 | 701.95500086538742 |

14 | 701.9550008653874 |

13 | 701.955000865387 |

12 | 701.95500086539 |

11 | 701.9550008654 |

10 | 701.955000865 |

8 | 701.95500087 |

7 | 701.9550009 |

6 | 701.955001 |

5 | 701.95500 |

4 | 701.9550 |

3 | 701.955 |

2 | 701.96 |

1 | 702.0 |

0 | 702 |

- ↑ Alpha: log2(3/2)*1200 gives 701.95500086538741774448673273737981051177728923097727254690318544

## See also

- Wikipedia: Rounding
- Wikipedia: Rounding #Round half away from zero – commercial rounding