Percentage error and significant figure

[mrcotton]

Homework Statement

If a diameter of 15.5 +/- 0.1mm has been quoted and you need to turn this to a percentage error
you get (0.1/15.5)*100 = 0.645...

so you would quote this as a percentage error of 0.6%

If it was 15.3 +/- 0.1mm and again you wanted percentage error
(0.1/15.3)*100 = 0.653...

So you would quote as 0.7%

So this is not to do with significant figures but the decimal place in which the uncertainty manifests?

I would be grateful if someone could tell me if this logic is correct

Thanks

 

[mfb]

The accuracy of "0.6%" is just "something between 0.55% and 0.65%", so steps of 0.1% can happen. The figure is right ("significant") in both cases.
As intermediate result, I would probably give 0.65% as uncertainty in both cases.

 

[haruspex]

The uncertainty in the uncertainty is not constrained by the original uncertainty. If you are quite certain that the error in the 15.5 number is no more than +/-.1, you can quote that as a percentage with as many digits as you like. But if you want to retain the level of guarantee in the original data, you must round it up, not to the nearest. E.g. .65%, .66% respectively.