**Standard Rounding Rules for Common
Arithmetic Operations**

by Christopher L. Mulliss

**The Standard Rounding Rules**

Operation |
Rounding Rule |
Accuracy |
Failure Modes |

Addition and Subtraction |
The number of decimal places in the result equals the smallest number of decimal places in the input numbers. |
100% for a series of up to 9 numbers |
· None for a series of 2 to 9 numbers · Can predict too many digits for a series of 10 or more numbers |

Multiplication |
The number of significant figures in the result equals the smallest number of significant figures in the input numbers. |
31.0% |
· Predicts 1 less digit than justified 68.8% of the time · Predicts 1 more digit than justified 0.2% of the time |

Division |
(Same as Multiplication) |
45.3% |
· Predicts 1 less digit than justified 54.4% of the time · Predicts 1 more digit than justified 0.3% of the time |

Common Logarithm |
The number of significant decimal places in the result equals one plus the number of significant digits in the input. |
57.18% |
· Predicts 1 more digit than justified 42.82% of the time |

Natural Logarithm |
The number of significant decimal places in the result equals the number of significant digits in the input. |
97.00% |
· Predicts 1 more digit than justified 3.00% of the time |

Common Exponential |
The number of significant digits in the result equals the number of significant decimal places in the input minus one. |
0.00% |
· Predicts 2 fewer digits than justified 61.46% of the time · Predicts 1 less digit than justified 38.54% of the time |

Natural Exponential |
The number of significant digits in the result equals the number of significant decimal places in the input. |
2.11% |
· Predicts 1 less digit than justified 97.89% of the time |

Green = Safe and Accurate, Red = Unsafe and/or Inaccurate