Physics quiz question: cubic centimeter equivalent of a gallon

Physics 205A Quiz 1, fall semester 2015
Cuesta College, San Luis Obispo, CA

According to the National Institute of Standards and Technology[*], the U.S. liquid gallon is defined to be exactly 231 in³, and the inch is defined to be exactly 2.54 cm. A U.S. liquid gallon is equivalent to:
(A) 7.09396709×10^–2 cm³.
(B) 1.40964848859×10¹ cm³.
(C) 5.8674×10² cm³.
(D) 3.785411784×10³ cm³.

[*] nist.gov/pml/wmd/pubs/upload/HB130-11-final.pdf.

Correct answer (highlight to unhide): (D)

Then setting up conversion factors such that unwanted units cancel (gallon, inches) while desired units remain (centimeters):

1 gallon = 231 in³·(2.54 cm/1 in)·(2.54 cm/1 in)·(2.54 cm/1 in),

such that:

1 gallon = 3.785411784×10³ cm³.

Since the 1 in = 2.54 cm conversion factor is exact, then presumably this equivalent amount of cm³ for 1 gallon retains all figures as significant.

Sections 70854, 70855, 73320
Exam code: quiz01rdBL
(A) : 0 students
(B) : 0 students
(C) : 13 students
(D) : 66 students

Success level: 83%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.46