Answer
(a) 2.16 x 10$^2$
(b) 3.7 x 10$^{-2}$
(c) 0.224
(d) 0.4
Work Step by Step
(a) 17.2 x 12.55 = 215.86
The number in the original problem with the least significant figures is 17.2, which has three significant figures. Therefore, we need to reduce the answer 215.86 to three significant figures. We look at the three significant figures, which are 2, 1, and 5. We also look at the digit that is to the right of the 5, which is an 8. We then round 5 up to 6, so we have the answer as 216. We represent the number in scientific notation to make it easier to identify the significant figures, so we have 2.16 x 10$^2$.
(b) First, we want to multiply 1.4 by 1.11 to get 1.554. We then divide that by 42.33 to get 0.037. The number in the original problem with the least number of significant figures is 1.4, which has two significant figures; therefore, our answer must have two significant figures only. We then represent the answer using significant figures, so we have 3.7 x 10$^{-2}$.
(c) We multiply 18.33 by 0.0122 to get 0.223626. The number in the problem that has the least number of significant figures is 0.0122, which is three; therefore, we should have three significant figures in the answer. We look at the first three significant figures: 2, 2, and 3.
We then look to the digit to the right of the 3, which is a 6; therefore, we have to round the 3 up to 4. The answer we get rounded to three significant figures is 0.224.
(d) We subtract 25.25 from 25.7 to get 0.45. In a subtraction problem, we need to express the answer to the same number of decimal places as the number in the original problem with the least number of decimal places, 25.7, which has only one decimal place. Since the digit to the right of the 4 is a 5, we will round to even, which would leave us with 0.4 as the answer rounded to one decimal place.
