This problem is from an intro college chemistry book.

"Each of the following calculations contains the numbers 4.2, 5.30, 11, and 28. The numbers 4.2 and 5.30 are measured quantities, and 11 and 28 are exact numbers. Do each calculation and express each number to the proper number of significant figures."

Problem (a) (4.2 + 5.30) X (28 +11)

The first operation is addition so the add/subt rules apply, i.e., sig fig to the 10ths place. The answer is 9.50, but I did not round off yet because the textbook also states that rounding off should only be done when all operations are complete.

The second operation (28 + 11) = 39 but is irrelevant to sig figs, since both numbers are exact.

9.50 X 39 = 370.5.

In mult/div the number with the fewest sig figs is controlling. This is 9.50 which has 3, therefore 370 is the answer.

Problem (c) 28-4.2/5.30X11

28-4.2: The add/sub rule gives sig fig to the 10th place: 23.8

5.30X11: the mult/div rule gives 3 sig figs. 58.3

Final operation: 23.8/58.3 = 0.40823327615

mult/div rule allows 3 sig figs, therefore 0.408.

Problem (d) 28-4.2/11-5.30 = 23.8/5.70 = 4.175438596649

Since division was the final op, this allows 3 sig figs: 4.18.

My question in these problems is whether sig figs are determined by the nature of the final operation, which I believe to be the case.