Match the mathematical operation with the rule for maximum error propagation. List - I List - II (P) Absolute error in Z = A + B (1) A Δ A + B Δ B (Q) Absolute error in Z = A − B (2) Δ A + Δ B (R)

Question

Match the mathematical operation with the rule for maximum error propagation.

List - I	List - II
(P) Absolute error in $Z = A + B$	(1) $\frac{Δ A}{A} + \frac{Δ B}{B}$
(Q) Absolute error in $Z = A - B$	(2) $Δ A + Δ B$
(R) Fractional error in $Z = A \times B$	(3) $\frac{Δ A}{A} - \frac{Δ B}{B}$
(S) Fractional error in $Z = A / B$	(4) $∣Δ A - Δ B ∣$

TestHub · Accepted Answer

For addition Z = A + B , the maximum absolute error is Δ Z = Δ A + Δ B (P-2). For subtraction Z = A − B , the maximum absolute error is also Δ Z = Δ A + Δ B (Q-2). For multiplication Z = A × B , the maximum fractional error is Z Δ Z ​ = A Δ A ​ + B Δ B ​ (R-1). For division Z = A / B , the maximum fractional error is also Z Δ Z ​ = A Δ A ​ + B Δ B ​ (S-1).

Physics - Error Question with Solution | TestHub

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