Assume that X, Y, and Z are independent measurements, and that the relative uncertainty in X is 5%, the relative uncertainty in Y is 10%, and the relative uncertainty in Z is 15%. Find the relative uncertainty in each of the following quantities:
a. XYZ
b. 
c. 
The relative uncertainty in X is 
= 0.05, the relative uncertainty in Y is 
= 0.10, and the relative uncertainty in Z is 
= 0.15.
(a) Let U = XY/Z, so lnU = lnX + lnY?lnZ.
The relative uncertainty in U is 19%.
(b) 
The relative uncertainty in U is 24.5%.
(c)
The relative uncertainty in U is 6.2%.
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