Physics quiz question: significant figures calculation

Physics 205A Quiz 1, fall semester 2017
Cuesta College, San Luis Obispo, CA

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

3.711 × ((2.5 – 1.80)/(2.5 + 1.80)) = ?

(A) 0.6041.
(B) 0.604.
(C) 0.60.
(D) 0.6.

Correct answer (highlight to unhide): (D)

For addition and subtraction operations, the term with the least number of decimal places (shown in gray) determines the number of significant decimal places in the result. Since 2.5 has decimal place, while 1.80 has two decimal places, then the subtraction operation in the numerator, and the addition operation in the denominator will both be limited to one decimal place:

3.711 × ((2.5 – 1.80)/(2.5 + 1.80)) = 3.711 × ((0.70)/(4.30)).

For both the numerator and denominator, the tenths decimal place is the least significant, while the hundredths place is insignificant. Since dividing the numerator by the denominator to evaluate the fraction will be limited by significant figures, we denote the only one significant figure (the tenths decimal place) in the numerator (denoted in green); the denominator has two significant figures (the ones and the tenths decimal places), and the hundredths decimal place for both numerator and denominator are insignificant, (denoted in yellow). Evaluating this fraction division will result in a number that will have only one significant figure:

3.711 × ((0.70)/(4.30)) = 3.711 × ((0.70)/(4.30)) = 3.711 × 0.1627906977,

and although 3.711 has four significant figures, it is multiplied by a quantity that has only one significant figure, and so the final answer must be expressed with one significant figure:

3.711 × 0.1627906977 = 0.6041162791 = 0.6.

Sections 70854, 70855
Exam code: quiz01D4mP
(A) : 7 students
(B) : 1 student
(C) : 18 students
(D) : 32 students

Success level: 55%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.32