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Chapter 1: Problem 39

Carry out the following operations, and express the answers with the appropriate number of significant figures. (a) \(14.3505+2.65\) (b) \(952.7-140.7389\) (c) \(\left(3.29 \times 10^{4}\right)(0.2501)\) (d) \(0.0588 / 0.677\)

Short Answer

Expert verified
(a) 16.00 (b) 811.96 (c) \(8.23 \times 10^{4}\) (d) 0.0869

Step by step solution

01

(a) 14.3505 + 2.65

To add numbers, align the decimals and add. However, we need to remember the significant figures rule for addition and subtraction: round your answer to the least number of decimal places of any number in the problem. 14.3505 + 2.65 --------- 16.0005 (not rounded) Now, we will round the result to the least number of decimal places, which, in this case, is 2. Final answer: 16.00
02

(b) 952.7 - 140.7389

For subtraction, align the decimals and subtract, then use the same significant figures rule for addition mentioned in part (a). 952.7 -140.7389 ----------- 811.9611 (not rounded) The least number of decimal places in the problem is 1, so we will round our answer to 1 decimal place. Final answer: 811.96
03

(c) (3.29 x 10^4) (0.2501)

For multiplication, multiply the numbers as normal but follow the significant figures rule for multiplication and division: round your answer to the least number of significant figures of any number in the problem. (3.29 x 10^4) (0.2501) = 822650 We have 3 significant figures in the first number (3.29) and 4 significant figures in the second (0.2501), so the result should have 3 significant figures. Final answer: 8.23 x 10^4
04

(d) 0.0588 / 0.677

For division, divide the numbers as normal and use the same significant figures rule for multiplication mentioned in part (c). 0.0588 / 0.677 = 0.086850809289 We have 3 significant figures in both the numerator (0.0588) and the denominator (0.677), so our final answer should have 3 significant figures as well. Final answer: 0.0869

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