Hi,
According to official regulations and guidelines (GUM, Supplement 1 to the GUM, EA-4/02) the numerical values of the measurement results should be rounded to be consistent with their uncertainties.
This means, you can report the measured result with less or the same decimal places as the uncertainty, but never with more decimal places.
What you suggest is the opposite of the prescriptions in the standard - you are rounding the uncertainty by using as reference the measured value.
This is totally wrong, because the uncertainty is the defining parameter in the rounding procedure.
The complete result in this example should be: (1000 ? 0.58) g or (1000 ? 0.6) g
You are quoting section 7.2.6 of the GUM. The example given in that paragraph shows a situation where the measurement result has more precision than the uncertainty. As the example follows, the measurement result is rounded to match the precision of the uncertainty.
I would argue that 7.2.6 doesn't specifically address a situation where the measurement result has
less precision than the uncertainty. What I consider to be "consistent" is when the precision of the measurement result and uncertainty match. Look in any guide on measurement uncertainty and it will be written that measurement uncertainty should be expressed as, at most, two sig-figs. It is necessary that the measurement result and reported uncertainty have the same precision for the sake of
significance arithmetic.
Using significant figures rules, the result is rounded to the position of the least significant digit in the most uncertain of the numbers when adding or subtracting. For example:
1000. + 0.58 = 1000.
1000. - 0.6 = 1000.
1000. + 1. = 1001.
For the result to show no impact of uncertainty is to suggest that there is no uncertainty, which is erroneous. Considering uncertainties are the result of statistical calculations and sig-fig rules are used for scientific and statistical calculations, it should go without saying that significance arithmetic is extremely relevant here.
You said, "...you can report the measured result with less or the same decimal places as the uncertainty..." I would have to disagree with the "less decimal places" part.