So I was refreshing my physics knowledge and someone gave me a question about uncertainty. I figured it would be easy, right? So I calculated the uncertainty from the error bars of raw data, and got roughly ±0.03. However, the units were only measured to the tenths place. Now I was always taught that your uncertainty must go to the same decimal place as the measured data. So how would this work? Would I round down to ±0.0? Would I leave it as ±0.03? Thank you very much for your help!
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The trouble with truncating answers is that the $\pm$ is an indicator of accuracy that should not have more decimal places than the precision of the gross result. There is no harm in expressing numbers such as in a format like $0.234\pm0.03$ for example.
Why? Often the $\pm$ number is a lot less accurate than the first or gross number because it is derivative by nature and thus less exact than the measurements themselves. Expressing the first number with less precision than the second, is however an error of overly aggressive truncation, which is a more serious error than specifying too many decimal places because the latter can be corrected by truncation but the former cannot, truncated numbers cannot be unerased.
Carl
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