Physics quiz question: comparing significant figures in arithmetic operations

Physics 205A Quiz 1, fall semester 2016
Cuesta College, San Luis Obispo, CA

Determine the arithmetic expression resulting in the greatest number of significant figures.
(A) (14.2 ÷ 0.55) – 7.30.
(B) (14.2 × 0.55) + 7.30.
(C) (There is a tie.)
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (B)

For the division and multiplication operations, it is the term with the least number of significant figures (shown in green) that determines the number of significant figures in the result, such that for the first expression:

(14.2 ÷ 0.55) – ... = 25.818181818 – ....

Similarly for the second expression,

(14.2 × 0.55) + ... = 7.81 + ....

For the addition and subtraction operations, it is the term with the least number of decimal places (shown in gray) that determines the number of significant decimal places in the result, such that for the first expression:

25.818181818 – 7.30 = 18.518181818,

which because there are no significant decimal places for the first number, this result will have no significant decimal places, and is thus rounded to 19.

For the second expression,

7.81 + 7.30 = 15.11,

which because there is only one significant decimal place for the first number, this result can only have one significant decimal place, and is thus truncated to 15.1.

Finally, comparing the numerical result from the first expression (19, which overall has two significant figures) with the numerical result from the second expression (15.1, which overall has three significant figures), evaluating the second expression results in the greater number of significant figures.

Sections 70854, 70855, 73320
Exam code: quiz01bIR6
(A) : 6 students
(B) : 18 students
(C) : 31 students
(D) : 0 students

Success level: 32%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.40