Question

prove that when two quantities are multiplied, the relative error in the result is the sum of the relative errors in the individual quantities​

Answer 1

Explanation:

When two quantities are added or subtracted, the absolute error in the final result is the sum of the absolute errors in the individual quantities. Z = A + B

We have by addition, Z ± ΔZ = (A ± ΔA) + (B ± ΔB).

The maximum possible error in Z

ΔZ = ΔA + ΔB

For the difference Z = A – B, we have

Z ± Δ Z = (A ± ΔA) – (B ± ΔB) = (A – B) ± ΔA ± ΔB

or, ± ΔZ = ± ΔA ± ΔB The maximum value of the error ΔZ is again ΔA + ΔB