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