Physics quiz question: marathon distance

Physics 205A Quiz 1, fall semester 2013
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Comprehensive Problem 1.57

Evaluate the following calculation, using an appropriate number of significant figures and/or decimal places.

(4.5760×10⁴ yd + 385 yd) × ((0.9144 m)/(1 yd)) = ?

(A) 4.219×10⁴ m.
(B) 4.2194×10⁴ m.
(C) 42,194.988 m.
(D) 42,194.9880 m.

Correct answer (highlight to unhide): (A)

Before adding 4.5760×10⁴ yd and 385 yd, they must first be expressed with the same power of ten, such that:

4.5760×10⁴ yd + 385 yd = 45,760 yd + 385 yd.

Both these numbers have no decimal places, so the result of this addition is simply 46,145 yd, with no decimal places (as the number of decimal places in addition and subtraction operations are limited by the quantity with the least number of decimal places, this case, zero). Note that 46,145 yd has five significant figures (denoted in green).

0.9144 m has four significant figures (the leading zero to the left of the decimal point is shown in yellow as it is not significant), while the "1 yd" value is part of an exact conversion factor, and has an infinite number of significant figures. The final result is then limited to four significant figures, as the number of significant figures in multiplication and division operations are limited by the quantity with the least number of significant figures, which in this case is four).

46,145 yd × (0.9144 m)/1 yd)) = 42,194.988 m = 4.219×10⁴ m.

(N.b. this is a calculation to convert the yards in a marathon into meters.)

Sections 70854, 70855, 73320
Exam code: quiz01cH3E
(A) : 59 students
(B) : 15 students
(C) : 1 student
(D) : 1 student

Success level: 78%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.50