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Chemistry Forums for Students => Analytical Chemistry Forum => Topic started by: Mager on October 06, 2017, 04:43:32 PM

Title: Propagation of Uncertainty
Post by: Mager on October 06, 2017, 04:43:32 PM
When propagating uncertainty for the multiplication of a value with uncertainty and a value without uncertainty (a constant) what is the proper procedure so the uncertainty in the result is scaled appropriately?

Here is my example and way I have approached it:

0.0160 (+/- 4E-4) * 4

First I considered the value according to the percent uncertainty such as 0.0160 (+/- 0.025) and then carried out the multiplication.

My result:  0.064 (+/- 0.025) (as the relative uncertainty)
                 0.064 (+/- 0.0016) (as reported with absolute uncertainty)

Im hoping someone can confirm this is the correct procedure and if not please let me know how to consider this calculation.
Title: Re: Propagation of Uncertainty
Post by: mjc123 on October 09, 2017, 04:33:53 AM
You are correct: multiply the absolute error by the constant; relative error is the same.
However, I would not report the relative uncertainty as 0.064 +/- 0.025. That might be confused with an absolute uncertainty. I would say 0.064 +/- 2.5%, or make it very clear in words, e.g. "0.064 with a relative uncertainty of +/- 0.025"