Propagation of relative uncertainties for Young's modulus Steps:

• Compute relative uncertainties: δm/m = 0.02/2.00 = 0.01; δd/d = 0.01/2.02 ≈ 0.005 (assuming standard precision for d); δe/e = 0.2/7.0 ≈ 0.029.
• For cross-sectional area A ∝ d², relative uncertainty δA/A = 2 × 0.005 = 0.010.
• Young's modulus E ∝ m/(A e) (L exact), so relative uncertainty δE/E = δm/m + δA/A + δe/e = 0.01 + 0.010 + 0.029 = 0.049.
• Absolute uncertainty δE = 0.049 × 1.61 × 10^{11} ≈ 0.079 × 10^{11}, expressed as 0.07 × 10^{11} with one significant figure.

Why D is correct:

• Matches maximum percentage uncertainty propagation formula for quotients/products, where relative errors add absolutely.

Why the others are wrong:

• A. Too small; ignores full contribution from e (2.9%).
• B. Too small; corresponds to root-sum-square (quadrature) method, not maximum error.
• C. Formatting error (missing parentheses); value overestimates by including unadjusted d error.

Final answer: D