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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 one plus the smallest number of significant figures in the input numbers.

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 one plus the number of significant decimal places in the input.

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

 

Reference: http://www.angelfire.com/oh/cmulliss/index.html