Physics quiz question: unit conversion discrepancies

Physics 8A Quiz 1, Spring Semester 2005
Cuesta College, San Luis Obispo, CA

Physics 8A learning goal Q1.2

(Cf. Young and Freeman, University Physics, 11/e, Exercise 1.15.)

[3.0 points.] Compare the exact relation of 1 inch = 2.54 cm with the approximate relation 39.37 inches = 100 cm. Which one of the following choices best corresponds to the percent discrepancy between using these relations to determine how many inches there are in one meter?
(A) 0 %.
(B) 0.0002%.
(C) 0.0079%.
(D) 0.01%.

Correct answer: (A)

The "observed" value of inches in one meter would be 39.37 inches, while the "expected" value would be based on the 1 inch = 2.54 cm relation:

1 m * (100 cm/1 m) * (1 inch/2.54 cm) = 39.370078740157... inches.

Then the difference between the observed and expected value would be:

39.37 inches - 39.370078740157... inches = 0.000078740157... inches,

or two decimal places, 0.0 inches. This makes the percent discrepancy 0%, to the correct number of significant figures.

Response (B) uses too many significant figures; response (C) does not divide by the expected value in converting the discrepancy into percent discrepancy; response (D) is as (C), but rounded up.

Student responses:
(A) : 15 students
(B) : 34 students
(C) : 10 students
(D) : 10 students