Physics quiz question: unit conversion and significant figures

Physics 205A Quiz 1, spring semester 2009
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 1.31

Evaluate the following calculation, and express the answer in units of m^3, using an appropriate number of significant figures and/or decimal places.

(3.2 m) * (1.242 cm) * (6.0*10^3 m) = ?

(A) 2*10^2 m^3.
(B) 2.4*10^2 m^3.
(C) 2*10^4 m^3.
(D) 2.4*10^4 m^3.

Correct answer: (B)

1.242 cm must be converted to 1.242*10^-2 m. Also the first and third lengths are expressed to only two significant figures, which will limit the final answer to two significant figures.

Response (A) does not have the correct number of significant figures. Response (D) has the correct number of significant figures, but cm was not converted to m. Response (C) has both an incorrect number of significant figures, and no cm to m conversion.

Student responses
Sections 30880, 30881
(A) : 3 students
(B) : 34 students
(C) : 0 students
(D) : 13 students

"Difficulty level": 68%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.50