Question

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. \(\frac{2.00 \times 10^{6}}{3.00 \times 10^{-7}}\)

Short answer

The short answers for the given mathematical operations are: a. \(2.22\) b. \(8.4 \times 10^{22}\) c. \(1.5 \times 10^{4}\) d. \(6.67 \times 10^{12}\)

Step-by-step solution

Make sure the numbers have the correct number of significant figures

First, identify the given numbers: \(0.102\) has 3 significant figures, \(0.0821\) has 4 significant figures, \(273\) has 3 significant figures, and \(1.01\) has 3 significant figures.

Perform the calculation

Multiply the numbers in the numerator and divide by the denominator, keeping track of the least number of significant figures: \(\frac{0.102 \times 0.0821 \times 273}{1.01} \approx 2.22\) Since the least number of significant figures is 3, the result has 3 significant figures: \(2.22\). #b. Calculate \(0.14 \times 6.022 \times 10^{23}\)#

Make sure the numbers have the correct number of significant figures

First, identify the given numbers: \(0.14\) has 2 significant figures, and \(6.022 \times 10^{23}\) has 4 significant figures.

Perform the calculation

Multiply the given numbers, keeping the least number of significant figures: \(0.14 \times 6.022 \times 10^{23} \approx 8.4 \times 10^{22}\) Since the least number of significant figures is 2, the result has 2 significant figures: \(8.4 \times 10^{22}\). #c. Calculate \(4.0 \times 10^{4} \times 5.021 \times 10^{-3} \times 7.34993 \times 10^{2}\)#

Make sure the numbers have the correct number of significant figures

First, identify the given numbers: \(4.0 \times 10^{4}\) has 2 significant figures, \(5.021 \times 10^{-3}\) has 4 significant figures, and \(7.34993 \times 10^{2}\) has 6 significant figures.

Perform the calculation

Multiply the given numbers, keeping the least number of significant figures: \(4.0 \times 10^{4} \times 5.021 \times 10^{-3} \times 7.34993 \times 10^{2} \approx 1.5 \times 10^{4}\) Since the least number of significant figures is 2, the result has 2 significant figures: \(1.5 \times 10^{4}\). #d. Calculate \(\frac{2.00 \times 10^{6}}{3.00 \times 10^{-7}}\)#

Make sure the numbers have the correct number of significant figures

First, identify the given numbers: \(2.00 \times 10^{6}\) has 3 significant figures, and \(3.00 \times 10^{-7}\) has 3 significant figures.

Perform the calculation

Divide the numbers, keeping the least number of significant figures: \(\frac{2.00 \times 10^{6}}{3.00 \times 10^{-7}} \approx 6.67 \times 10^{12}\) Since both numbers have 3 significant figures, the result also has 3 significant figures: \(6.67 \times 10^{12}\).