Question

Evaluate each of the following, and write the answer to the appropriate number of significant figures. a. (0.0432)(2.909)\(\left(4.43 \times 10^{8}\right)\) b. \((0.8922) /\left[(0.00932)\left(4.03 \times 10^{2}\right)\right]\) c. \(\left(3.923 \times 10^{2}\right)(2.94)\left(4.093 \times 10^{-3}\right)\) d. \((4.9211)(0.04434) /\left[(0.000934)\left(2.892 \times 10^{-7}\right)\right]\)

Short answer

The short answers to the given expressions are: a. \(1.255 \times 10^{10}\) b. \(0.2377\) c. \(1.449 \times 10^{4}\) d. \(8.08 \times 10^{5}\)

Step-by-step solution

a. Evaluate the expression and write the answer in the appropriate number of significant figures.#

The expression is: a. \((0.0432)(2.909)\)\(\left(4.43 \times 10^{8}\right)\) First, multiply the numbers together: \[(0.0432)(2.909)(4.43 \times 10^{8}) = 0.12548608 \times 10^{8}\] Now, we need to round our answer to the correct number of significant figures. Each of the factors has four significant figures, so our result should have four significant figures as well. Therefore, the answer is: \[1.255 \times 10^{10}\]

b. Evaluate the expression and write the answer in the appropriate number of significant figures.#

The expression is: b. \((0.8922) /\left[(0.00932)\left(4.03 \times 10^{2}\right)\right]\) First, multiply the denominator numbers together, then divide: \[(0.8922)/[(0.00932)(4.03 \times 10^{2})] = 0.8922 / (0.03750696 \times 10^{2}) = 0.8922 / 3.750696\] Now, we need to round our answer to the correct number of significant figures. Both the numerator and the denominator have four significant figures, so our result should have four significant figures as well. Therefore, the answer is: \[0.2377\]

c. Evaluate the expression and write the answer in the appropriate number of significant figures.#

The expression is: c. \(\left(3.923 \times 10^{2}\right)(2.94)\left(4.093 \times 10^{-3}\right)\) First, multiply the numbers together: \[ (3.923 \times 10^{2})(2.94)(4.093 \times 10^{-3}) = 1203.822 \times 12.04082\] Now, we need to round our answer to the correct number of significant figures. Each of the factors has four significant figures, so our result should have four significant figures as well. Therefore, the answer is: \[1.449 \times 10^{4}\]

d. Evaluate the expression and write the answer in the appropriate number of significant figures.#

The expression is: d. \((4.9211)(0.04434) /\left[(0.000934)\left(2.892 \times 10^{-7}\right)\right]\) First, multiply the numerator numbers together: \[(4.9211)(0.04434) = 218.2125634\] Next, multiply the denominator numbers together: \[(0.000934)(2.892 \times 10^{-7}) = 0.00027004008\] Now, divide the two results: \[218.2125634 / 0.00027004008 = 808022.2456\] Lastly, we need to round our answer to the correct number of significant figures. The number with the least significant figures in the expression is 3, so our result should also have three significant figures. Therefore, the answer is: \[8.08 \times 10^{5}\]