Question

If the measured values of two quantities are A ± ∆A and B ± ∆B, ∆A and ∆B being the mean absolute errors. What is the maximum possible error in A ± B? Show that if Z = A/B

ΔZ/Z = ΔA/A + ΔB/B

Answer 1

Maximum possible error in (A ± B) is (∆A + ∆B).

Errors in divisions:

i) A

Suppose, Z = A/B and measured values of A and B are (A ± ∆A) and (B ± ∆B) then,

As, ∆B/B << 1, expanding using Binomial theorem,

∴ Maximum relative error of

ii) Thus, when two quantities are divided, the maximum relative error in the result is the sum of relative errors in each quantity.