Hi Charles.

This is news to me. It really depends on the application and industry you are involved in and what exactly you are measuring. Often in mathematics we can take our cues from the implied precision of the known values from the question. An entire branch of science is given to understanding the limits of precision (also called uncertainty) in measurements and analysis of lab results. The basic premise is that you can't come up with an "answer" that is more precise than the measurements used to calculate the answer.

For example, if your meter stick only has gradations to the millimeter, you can't measure tenths of millimeters with it precisely. If you use that distance measurement to calculate a speed, the uncertainty in the speed must reflect the uncertainty in the distance and time you used to calculate it.

When you report a measurement or calculation resulting in 12.345, then you are indicating that it is precise down to the last digit (often we will use a +/- value to indicate more specific uncertainties, like 12.345 +/- 0.005).

Remember though: it depends on what you are using the measurement for. Can you imagine the results if an insurance decided that the chance of a major hurricane striking a large city was 0.0003 but rounded it to 3 decimal places: 0.000?

Stephen La Rocque