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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

 

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