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