## 20180827

### Physics quiz question: significant figures calculation

Physics 205A Quiz 1, fall semester 2018
Cuesta College, San Luis Obispo, CA

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

(125÷33.814) – (217×0.0163871) = ?

(A) 0.14.
(B) 0.141.
(C) 0.1407.
(D) 0.1406930.

Correct answer (highlight to unhide): (A)

Here 125 has three significant figures, 33.814 has five significant figures, 217 has three significant figures, and 0.0163871 has six significant figures (as denoted in green).

For multiplication and division operations, the term with the least number of significant figures determines the number of significant figures in the result, such that both parenthesis will have only three significant figures:

(3.6966936772) – (3.5560007).

For addition and subtraction operations, the rule is to limit your answer to the right-most digit that is the result from all significant digits. Remember that it's just better to see how this works, rather than memorizing the statement of the rule itself.

Let's write these numbers as a "stack," aligning them properly for subtraction:

 3.6966936772 – 3.5560007 = ?

Since only the ones, one-tenths and one-hundredths columns have all non-blank significant digits in the "stack," they will all be significant in the final answer. (The remaining digits from the one-thousandths place onwards are not significant, from the previous application of the multiplication/division rule.)

 3.6966936772 – 3.5560007 = 0.1406929772

Since we ignore the placeholder "0" to the left of the decimal point, the result has only two significant figures, expressed as 0.14.

(This calculation is the apparent discrepancy, in liters, between two different definitions of the Irish barrel, given as 125 oz or 217 in3, cf. wki.pe/Gallon#English_system_gallons.)

Sections 70854, 70855
Exam code: quiz01CrR4
(A) : 37 students
(B) : 20 students
(C) : 3 students
(D) : 2 students

Success level: 60%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.70