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Chapter 1: Problem 35

Evaluate each of the following, and write the answer to the appropriate number of significant figures. a. \(212.2+26.7+402.09\) b. \(1.0028+0.221+0.10337\) c. \(52.331+26.01-0.9981\) d. \(2.01 \times 10^{2}+3.014 \times 10^{3}\) e. \(7.255-6.8350\)

Short Answer

Expert verified
The answers for each problem are as follows: a. \(641.0\) b. \(1.327\) c. \(77.34\) d. \(3215\) e. \(0.420\)

Step by step solution

01

Problem 1: a

Evaluate \(212.2 + 26.7 + 402.09\). Notice that the number with the least decimal places is 26.7, having only one decimal place. Perform the addition and round the sum to one decimal place: \(212.2 + 26.7 + 402.09 = 641\boxed{.0}\).
02

Problem 2: b

Evaluate \(1.0028 + 0.221 + 0.10337\). Notice that the number with the least decimal places is 0.221, having three decimal places. Perform the addition and round the sum to three decimal places: \(1.0028 + 0.221 + 0.10337 = 1.32\boxed{7}\).
03

Problem 3: c

Evaluate \(52.331 + 26.01 - 0.9981\). Notice that the number with the least decimal places is 26.01, having two decimal places. Perform the addition and subtraction operations, rounding the sum to two decimal places: \(52.331 + 26.01 - 0.9981 = 77.3\boxed{4}\).
04

Problem 4: d

Evaluate \(2.01 \times 10^{2} + 3.014 \times 10^{3}\). First, we need to express both numbers in the same exponent form: \(201 + 3014\). Perform the addition operation: \(201 + 3014 = 32\boxed{15}\).
05

Problem 5: e

Evaluate \(7.255 - 6.8350\). Notice that the number with the least decimal places is 7.255, having three decimal places. Perform the subtraction operation and round the difference to three decimal places: \(7.255 - 6.8350 = 0.4\boxed{20}\).

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