Question

Find the absolute and percent relative uncertainty and express each answer with a reasonable number of significant figures.

A) 9.41 (±0.01) + 4.49 (±0.02) − 3.26 (±0.06) = ? absolute uncertainty & percent uncertainty

(b) 86.9 (±1.3) ✕ 36.5 (±0.3) ⁄ 21.1 (±0.2) = ? absolute uncertainty & percent uncertainty

(c) [4.79 (±0.01) − 1.99 (±0.01)] ⁄ 17.9 (±0.1) = ?absolute uncertainty & percent uncertainty

(d) 2.0223 (±0.0005) + 1.403 (±0.005) + 4.63 (±0.02) = ? absolute uncertainty & percent uncertainty

(e) 2.0223 (±0.0005) ✕ 10³ + 1.403 (±0.005) ✕ 10² + 4.63 (±0.02) ✕ 10¹ = ?absolute uncertainty & percent uncertainty

(f) [2.71 (±0.06)]^1/3 = ?absolute uncertainty & percent uncertainty

(g) log[2.71(±0.06)] = ?

Answer 1

A) 9.41 (+/-0.01) + 4.49 (+/-0.02) - 3.26 (+/-0.06) = absolute uncertainty = +/-0.09 ; percent relative uncertainty = +/-2.40%

B) 86.9 (+/-1.3) x 36.5 (+/-0.3)/21.1 (+/-0.2) = absolute uncertainty = +/-1.8 ; percent relative uncertainty = +/-3.3%

C) [4.79 (+/-0.01) - 1.99 (+/-0.01)]/17.9 (+/-0.1) = absolute uncertainty = +/-0.12 ; percent relative uncertainty = 1.27%

D) 2.0223 (+/-0.0005) + 1.403 (+/-0.005) + 4.63 (+/-0.02) = absolute uncertainty = +/-0.0255 ; percent relative uncertainty = 0.8131%

E) 2.0223 (+/-0.0005) x 10^3 + 1.403 (+/-0.005) x 10^2 + 4.63 (+/-0.02) x 10^1 = absolute uncertainty = +/-0.0255 ; percent relative uncertainty = 0.8131%

F) [2.71 (+/-0.06)]^1/3 = absolute uncertainty = +/-0.06 ; percent relative uncertainty = 2.21%

G) log[2.71 (+/-0.06)] = absolute uncertainty = +/-0.06 ; percent relative uncertainty = 1.27%