Error AnalysisHardQuestion 5043
Question
Positive measurements a and b have small maximum absolute error bounds δa and δb. What is the first-order maximum relative error in their product?
- Aδa/a − δb/b
- Bδa/a × δb/b
- Cδa/a + δb/bCorrect
- D(δa + δb)/(a × b)
Correct answer
δa/a + δb/b
Explanation
The first-order maximum relative-error estimate is δa/a + δb/b. This is a worst-case bound approximation, not the root-sum-of-squares rule for independent standard uncertainties.