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#### Mager

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##### Propagation of Uncertainty
« on: October 06, 2017, 10:43:32 AM »

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.
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#### mjc123

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##### Re: Propagation of Uncertainty
« Reply #1 on: October 08, 2017, 10:33:53 PM »

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"
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