**Recommended Rounding Rules for Common
Arithmetic Operations**

by Christopher L. Mulliss

The following list
provides a set of recommended rounding rules for general use based on almost 10
years of research by Christopher Mulliss and Dr. Wei Lee’s Team. The criteria used in selecting the rounding
rules are listed below:

1.
Rounding
rules should be as simple as possible.

2.
Rounding
rules should be as accurate as possible.

3.
Rounding
rules should predict the minimum number of significant digits needed to
preserve precision, while simultaneously avoiding gross overstatements of
precision.

**Recommend Rounding Rules for
General Use**

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 |
68.8% |
· Predicts 1 or 2 more digits than justified 31.2% of the time · Very rarely (< 1%) predicts 2 digits too many |

Division |
(Same as Multiplication) |
54.7% |
· Predicts 1 or 2 more digits than justified 45.3% of the time · Very rarely (< 1%) predicts 2 digits too many |

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 |
61.46% |
· Predicts 1 more digit than justified 38.54% of the time |

Natural Exponential |
(Same as Common Exponential) |
98.13% |
· Predicts 1 more digit than justified 1.87% of the time |

Green = Standard Rounding Rule, Aqua = Alternate Rounding Rule