Question

how many significant figures would this calculation have if it were completed: (9.04 - 8.23 + 21.954 + 81.0) × 3.1416 answer: a 3 b 4 c 5 d 6

Explanation:

Step1: Determine sig - figs in addition/subtraction

In addition and subtraction, we look at decimal places. 9.04 has 2 decimal places, 8.23 has 2 decimal places, 21.954 has 3 decimal places, and 81.0 has 1 decimal place. We go by the least number of decimal places among them for the result of addition/subtraction. So we perform $(9.04 - 8.23+21.954 + 81.0)=(0.81+21.954 + 81.0)=103.764\approx103.8$ (rounded to 1 decimal place). 103.8 has 4 significant figures.

Step2: Determine sig - figs in multiplication

In multiplication, the result has the same number of significant figures as the number with the least significant figures among the values being multiplied. 103.8 has 4 significant figures and 3.1416 has 5 significant figures. So the result of $103.8\times3.1416$ will have 4 significant figures.

Answer:

B. 4