Physics quiz question: solar intensity conversion

Physics 5A (currently Physics 205A) Quiz 1, spring semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Problem 1.16

The intensity of the sun's radiation that reaches Earth's atmosphere is 1.4 kW/m² (kW = kilowatt; W = watt). This intensity, in units of W/mm², is:
(A) 1.4×10^-6 W/mm².
(B) 1.4×10^-3 W/mm².
(C) 1.4 W/mm².
(D) 1.4×10³ W/mm².

Correct answer (highlight to unhide): (B)

Relevant conversion factors are 1 kW = 1,000 W and 1 m = 1,000 mm. Then setting up conversion factors such that unwanted units cancel (kW, m) while desired units remain (W, mm):

1.4 kW/m² = (1.4 kW/m²)·(1,000 W/1 kW)·(1 m/1,000 mm)·(1 m/1,000 mm) = 1.4×10^-3 W/mm².

Student responses
Sections 4987, 4988
(A) : 7 students
(B) : 6 students
(C) : 18 students
(D) : 8 students

Success level: 31%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.37