How to round off percentage uncertainties?

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SUMMARY

The discussion focuses on the correct method for rounding percentage uncertainties, specifically using the example of calculating the percentage uncertainty for a measurement of (225.7 +/- 0.5) mm. The calculation yields a percentage uncertainty of approximately 0.2215%. It is established that the percentage uncertainty should be rounded to one significant figure, resulting in a final value of 0.2%. The consensus emphasizes that the number of significant figures in the uncertainty should not exceed that of the least precise measurement.

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jayadds
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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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