that is exactly the information that an error bar is designed to convey, and as your metrologist has pointed out - the uncertainlty in your initial measurement has to be derived from somewhere. Whether that is a highly formal procees or an engineering estimate is irrelevant in this discussion, the important thing is the mindset that the uncertainty gets transformed along with the value. Once you have that mindset it can become obvious, say in the case above of converting the units for PCB pad placement, that if you do the conversion of the distance from each pad back to , say, pin 1, then you have the same uncertainlty in the position of each pad. But if you convert the distance between pin 1 & pin 2, then pin 2 to pin 3.. then the uncertainties grow with each successive calculation
@Roger, you need to carry that a step futher by adding a level of confidence.
Calibration and metrology people will tell you that your definition repeated blow is also meaningless. That is, with what level of confidence can you say that the actual value of a measurement is within the upperand lower tolerance limits? Are you 90% sure? 95% sure? 99.99% sure?
a measurement was totally meaningless unless it had an associated tolerance or error bar, and any calculation or transformation on the measurement must also be done on the tolerance figure, so at the end you know the accuracy bounds of your result - so no guessing how many decimal places to quote.
I'm so glad someone finally mentioned tolerances. I remember my tutor telling us at the end of the first year of my physics degree "we only tried to teach you one thing this year: the importance of error bars in measurement". They stressed that a measurement was totally meaningless unless it had an associated tolerance or error bar, and any calculation or transformation on the measurement must also be done on the tolerance figure, so at the end you know the accuracy bounds of your result - so no guessing how many decimal places to quote.
Many cheap digital calipers display to .001 inch and 0.1 mm, depending on selection of measurement units. Since 0.1 mm is approximately .004 inch, it is better to do the measurement using the inch display then convert to metric with a calculator - four times better resolution.
PCB design is another place where rounding can get you into trouble. For example when you're creating a footprint in mils from a drawing in mm. If you convert the average spacing to mils and round to the nearest mil and then place the pins using this average spacing, the pins at the end will be off. You need to convert each individual pin location from mm to mils and then round.