Higher-Accuracy Rounding Rules for
Common Arithmetic Operations
by Christopher L. Mulliss
The following list
provides a set of recommended rounding rules for higher-accuracy use based on almost
10 years of research by Christopher Mulliss and Dr. Wei Lee’s Team. The criteria used in this list emphasizes
accuracy over simplicity and even (in one case) over preservation of precision. The user should carefully apply these rules
only when their situation justifies it.
High Accuracy Rounding Rules
|
Operation |
Rounding Rule |
Accuracy |
Failure Modes |
|
Division |
The “Portuguese
Rule”: Count numbers whose leading digit is 5 or greater as having an extra significant digit and then apply the standard rule for division. |
68.99% |
· Predicts 1 less digit than justified 16.95% of the time · Predicts 1 more digit than justified 14.06% of the time |
|
Common Logarithm |
The Chen-Lee-Mulliss Rule for Common Logarithms: If the leading digit of the input is 4 or greater then the number of significant decimal places in the result equals one plus the number of significant digits in the input. Otherwise, the number of significant decimal places in the result equals the number of significant digits in the input. |
90.21% |
· Predicts 1 more digit than justified 9.79% of the time |
|
Common Exponential |
The Refined Chen-Lee-Mulliss Rule for Common Exponentials: If the leading digit of the result is 4 or smaller then the number of significant digits in the result equals one plus the number of significant decimal places in the input. Otherwise, the number of significant digits in the result equals the number of significant decimal places in the input. |
90.16% |
· Predicts 1 more digit than justified 9.84% of the time |
Red = Violations of
the
