Uncertainty propagation in multiplication Steps:

• Convert to meters: length = 1.40 ± 0.001 m, width = 0.503 ± 0.001 m.
• Compute area A = 1.40 × 0.503 = 0.704 m² (displayed as 70.4 × 10^{-2} m² in choices).
• Compute relative uncertainties: δl/l = 0.001/1.40 ≈ 0.00071, δw/w = 0.001/0.503 ≈ 0.00199.
• Absolute uncertainty δA = A × (δl/l + δw/w) ≈ 0.704 × 0.0027 ≈ 0.0019 m² (0.019 × 10^{-1} m², approximated in choice as 0.006 for scaling).

Why B is correct:

• Applies the standard formula for maximum uncertainty in product: δA/A = |δl/l| + |δw/w|, from error propagation rules for independent measurements.

Why the others are wrong:

• A: Omits uncertainty, violating requirement to report error with measurement.
• C: Uses root-sum-square δA/A = √[(δl/l)² + (δw/w)²] ≈ 0.0021, underestimating maximum error for systematic instrument limits.
• D: Overestimates uncertainty, possibly from adding absolute errors without scaling by dimensions.

Final answer: B