- #1
TheCanadian
- 367
- 13
I am just wondering why there is a discrepancy between two different methods for error propagation. For example, if you have ## Q = (a)(b)(c) ## then the relative error in Q is simply the square root of the sum of the squares of each of the terms being multiplied together, correct? But what if ## Q = (a)(a)(a) ##. Why isn't the relative error in Q now simply once again the square root of the sum of the squares of a (which in this case would be 3 terms)? I understand the derivation for the relative error in ## Q = a^3 ## being ## 3 \frac {\Delta a}{a} ## but just don't quite understand why the earlier rule pertaining to basic multiplication and division no longer applies. What is the reason for a discrepancy between the two methods of error propagation? Can't exponentiation (using positive integers) be considered as just an extension of multiplication?