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.
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.