When precision matters, that precision is considered in the measurements. You would never put 0.5 +- 0.208333, you express it as 0.50 +- 0.21. The error value is just the standard deviation of the measurements and it doesn't make sense to use more than 2 significant digits.

Another example would be measuring large distances using a ruler with centimeter precision. In that case, a measurement would be expressed as 250 +- 1 cm. Converting the measurement from cm to mm, it is 2500 +- 10 mm. This is much more cumbersome with inches or feet as changing units means updating the precision, possibly reducing it.