Perform the following mathematical operations, and express each result to the correct number of significant figures. a. \(\frac{0.102 \times 0.0821 \times 273}{1.01}\) b. \(0.14 \times 6.022 \times 10^{23}\) c. $4.0 \times 10^{4} \times 5.021 \times 10^{-3} \times 7.34993 \times 10^{2}$ d. \(\frac{2.00 \times 10^{6}}{3.00 \times 10^{-7}}\)

To multiply and divide numbers with significant figures: 1. Count the number of significant figures in each of the numbers, and note the one with the least number of significant figures. 2. Perform the requested operations (multiplication and division). 3. Round the result to the least number of significant figures noted earlier. Applying the above rules to the given problem: 1. Counting the significant figures of each number: 0.102 (3 significant figures), 0.0821 (4 significant figures), 273 (3 significant figures), and 1.01 (3 significant figures). 2. Perform the operations: \(\dfrac{0.102 \times 0.0821 \times 273}{1.01} = 2.17889908616187969\) 3. 0.102 has the least number of significant figures (3), so round the result to 3 significant figures: 2.18

To multiply numbers with significant figures: 1. Count the significant figures in each number, and note the one with the least number of significant figures. 2. Perform the requested operation (multiplication). 3. Round the result to the least number of significant figures noted earlier. Applying the above rules to the given problem: 1. Counting the significant figures of each number: 0.14 (2 significant figures), and 6.022 x 10^23 (4 significant figures). 2. Perform the operation: \(0.14 \times 6.022 \times 10^{23} = 8.4308 \times 10^{23}\) 3. 0.14 has the least number of significant figures (2), so round the result to 2 significant figures: \(8.4 \times 10^{23}\)

To multiply numbers with significant figures: 1. Count the significant figures in each number, and note the one with the least number of significant figures. 2. Perform the requested operation (multiplication). 3. Round the result to the least number of significant figures noted earlier. Applying the above rules to the given problem: 1. Counting the significant figures of each number: 4.0 x 10^4 (2 significant figures), 5.021 x 10^-3 (4 significant figures), and 7.34993 x 10^2 (6 significant figures). 2. Perform the operation: \(4.0 \times 10^4 \times 5.021 \times 10^{-3} \times 7.34993 \times 10^2 = 1470209.96\) 3. 4.0 x 10^4 has the least number of significant figures (2), so round the result to 2 significant figures: \(1.5 \times 10^6\)

To divide numbers with significant figures: 1. Count the number of significant figures in each of the numbers, and note the one with the least number of significant figures. 2. Perform the requested operation (division). 3. Round the result to the least number of significant figures noted earlier. Applying the above rules to the given problem: 1. Counting the significant figures of each number: 2.00 x 10^6 (3 significant figures) and 3.00 x 10^-7 (3 significant figures). 2. Perform the operation: \(\dfrac{2.00 \times 10^6}{3.00 \times 10^{-7}} = 6666666666.66667\) 3. Both numbers have the same number of significant figures (3), so round the result to 3 significant figures: \(6.67 \times 10^9\)