Show that the maximum error of two quantities is equal to the sum of the absolute errors in
the two individual quantities.
numan the distance and time ofan nhiert in
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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
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