## 20180828

### Physics quiz question: comparing significant figures in arithmetic operations

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

Determine the arithmetic expression resulting in the greater number of significant figures.
(A) (8,080 × 5.5) – 4.
(B) (8,080 ÷ 5.5) + 4.
(C) (There is a tie.)
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (C)

For the multiplication and division 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:

(8,080 × 5.5) – ... = 44,440 – ....

Similarly for the second expression,

(8,080 ÷ 5.5) – ... = 1,469.0909090909 + ....

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 the first expression as a "stack," aligning the numbers properly for subtraction:

 44,440 – 00,004 = ?

Since only the ten-thousands and thousands columns have all non-blank significant digits in the "stack," they will all be significant in the final answer. (The hundreds, tens, and ones columns are not significant, from the previous application of the addition/subtraction rule for the first number, and notably for the ones column, which has a non-significant digit and a significant digit.)

 44,440 – 00,004 = 44,436

Thus the result has only two significant figures, expressed as 4.4×104.

Similarly we write the second expression as a "stack" as well, aligning the numbers properly for addition:

 1,469.0909090909 + 0,004 = ?

Since only the thousands and hundred columns have all non-blank significant digits in the "stack," they will all be significant in the final answer. (The tens, ones, and all other columns to the right of the decimal point are not significant, from the previous application of the addition/subtraction rule for the first number, and notably for the ones column, which has a non-significant digit and a significant digit.)

 1,469.0909090909 + 0,004 = 1,473.0909090909

Thus the result also has only two significant figures, expressed as 1.5×103.

Sections 70854, 70855
Exam code: quiz01D4mP
(A) : 29 students
(B) : 9 students
(C) : 24 students
(D) : 0 students

Success level: 39%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.45