How Should Uncertainties Be Calculated When Multiplying Values Near Zero?

[max0005]

Homework Statement

Dear All,

Suppose I had to values: A (±a) and B (±b) where A not equal to a and B not equal to b. I have to find the product of A and B taking into consideration uncertainties.

Homework Equations

A (±a) * B (±b) = C (±c) where c = (a/A+b/B)

The Attempt at a Solution

My question would be: Suppose A and B represented change in mass of a sample. As A and/or B tended to zero the uncertainty would tend to infinite. Am I doing anything wrong?

max

 

[lewando]

I think your formula for c is suspect. I have seen and used c= A*B*sqrt((a/A)² + (b/B)²).

To avoid the divide by zero issue, add a small number to A or B (much smaller than a or b).

Your question is intriguing. This formula seems to work if either A or B is (almost) zero, but if A and B are both (almost) zero, the results do not compare very well, based on simulations.