Exact vs. Approximate Length Conversions
A conversion can have an exact underlying definition while its decimal display is rounded. Exactness of the unit relationship is different from precision of a measured value.
Exact definitions
The relationships 1 inch = 25.4 millimeters, 1 foot = 0.3048 meter, and 1 mile = 1,609.344 meters are exact. These numbers do not carry measurement uncertainty.
Rounded decimal displays
An exact ratio can produce a non-terminating decimal in one direction. One centimeter in inches repeats beyond any practical display, so the answer is shown to a selected number of digits.
The approximation symbol describes the displayed decimal, not a weakness in the unit definition.
Measured values have their own uncertainty
A board read as 24 inches on a ruler may be less certain than a calibrated instrument reading. Converting it to many decimal places does not create new information.
- Keep guard digits during intermediate calculations.
- Round once at the end.
- Match the final precision to the source measurement and the decision being made.
- Label mental estimates so they are not mistaken for specification values.
Questions about this topic
Is 1 centimeter exactly 0.3937 inch?
No. 0.3937 inch is a rounded display; the exact relationship comes from 1 inch = 2.54 centimeters.
Does an exact factor make a measured result exact?
No. The input measurement can still have uncertainty even when the conversion factor is exact.