How to round off percentage uncertainties?

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To round off percentage uncertainties, it is essential to adhere to the significant figures of the measured value. In the example provided, the percentage uncertainty calculated as 0.22153088% should be rounded to match the significant figures of the error, which is 1 significant figure in this case. Therefore, the appropriate rounding would yield 0.2% as the final percentage uncertainty. It is emphasized that one cannot use more significant figures than the least precise measurement. Proper error analysis requires justification for any deviation from this rounding convention.
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How to round off percentage uncertainties?

Here's is an example question:

Find the percentage of uncertainty in (225.7+/-0.5)mm.
I know that to find out percentage, it's simply 0.5/225.7 x 100 = 0.22153088...%

Now, my question is, how much do I round off for this percentage uncertainty? Should I just round it off to one significant figure? Or Is there a certain rule?
 
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strictly speaking you cannot use more sig figs than the smallest you are given/calculate...that is what the word 'significant' means (If they are not significant then they are insignificant !)
Your error is quoted as +/-0.5mm which means 1 significant figure so I would say round off to 0.2%
I would challenge anyone dealing with error analysis to justify that this should be given to 2 or 3 sig figs.
 

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