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Chapter 1: Problem 21

Perform the following calculations; express each answer in exponential form and with the appropriate number of significant figures. (a) \(0.406 \times 0.0023=\) (b) \(0.1357 \times 16.80 \times 0.096=\) (c) \(0.458+0.12-0.037=\) (d) \(32.18+0.055-1.652=\)

Short Answer

Expert verified
(a) \(9.3 \times 10^{-4}\), (b) \(2.2 \times 10^{-1}\), (c) \(5.4 \times 10^{-1}\), (d) \(3.058 \times 10^{1}\)

Step by step solution

01

Solve (a) - Perform the Calculation

Perform multiplication for \(0.406 \times 0.0023\), which will give the result 0.000934.
02

Solve (a) - Determine Number of Significant Figures

The number of significant figures in the final calculation must be the same as the number with the least significance in the original numbers. Here, \(0.0023\) has two significant figures, hence the answer will also be in two significant figures, which results in 0.00093.
03

Solve (a) - Convert to Exponential Form

Write the answer in exponential form to give \(9.3 \times 10^{-4}\).
04

Solve (b) - Perform the Calculation

Perform multiplication for \(0.1357 \times 16.80 \times 0.096\), which will give the result 0.22058.
05

Solve (b) - Determine Number of Significant Figures

Based on the rule for multiplication and division, the number of significant figures in the final calculation must equal the smallest number of significant figures in the original numbers. Hence in this case, the answer will be in two significant figures 0.22.
06

Solve (b) - Convert to Exponential Form

Convert the decimal to exponential notation, which will yield \(2.2 \times 10^{-1}\).
07

Solve (c) - Perform the Calculation

Perform the operations in order \(0.458 + 0.12 - 0.037\), which will yield 0.541.
08

Solve (c) - Determine Number of Significant Figures

The answer for addition and subtraction should be reported to the lowest decimal place contained in the original numbers. Hence, the answer should be reported to the hundredth place to yield 0.54.
09

Solve (c) - Convert to Exponential Form

Write the calculation in exponential form, which will yield \(5.4 \times 10^{-1}\).
10

Solve (d) - Perform the Calculation

Perform the operations in order \(32.18+0.055-1.652\), which will yield 30.583.
11

Solve (d) - Determine Number of Significant Figures

Because we are adding and subtracting, the final answer should be reported to the hundredth decimal place, 30.58.
12

Solve (d) - Convert to Exponential Form

The final answer will be in exponential form, \(3.058 \times 10^{1}\).

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Most popular questions from this chapter

Determine the number of the following: (a) square meters \(\left(\mathrm{m}^{2}\right)\) in 1 square kilometer \(\left(\mathrm{km}^{2}\right)\) (b) cubic centimeters \(\left(\mathrm{cm}^{3}\right)\) in 1 cubic meter \(\left(\mathrm{m}^{3}\right)\) (c) square meters \(\left(\mathrm{m}^{2}\right)\) in 1 square mile \(\left(\mathrm{mi}^{2}\right)\) \((1 \mathrm{mi}=5280 \mathrm{ft})\)

A lump of pure copper weighs \(25.305 \mathrm{g}\) in air and 22.486 g when submerged in water \((d=0.9982 \mathrm{g} / \mathrm{mL})\) at \(20.0^{\circ} \mathrm{C} .\) Suppose the copper is then rolled into a \(248 \mathrm{cm}^{2}\) foil of uniform thickness. What will this thickness be, in millimeters?

Indicate whether each sample of matter listed is a substance or a mixture; if it is a mixture, indicate whether it is homogeneous or heterogeneous. (a) clean fresh air (b) a silver-plated spoon (c) garlic salt (d) ice

Express the result of each of the following calculations in exponential form and with the appropriate number of significant figures. (a) \(\left(4.65 \times 10^{4}\right) \times\left(2.95 \times 10^{-2}\right) \times\left(6.663 \times 10^{-3}\right) \times 8.2=\) (b) \(\frac{1912 \times\left(0.0077 \times 10^{4}\right) \times\left(3.12 \times 10^{-3}\right)}{\left(4.18 \times 10^{-4}\right)^{3}}=\) {c} \(\left(3.46 \times 10^{3}\right) \times 0.087 \times 15.26 \times 1.0023=\) (d) \(\frac{\left(4.505 \times 10^{-2}\right)^{2} \times 1.080 \times 1545.9}{0.03203 \times 10^{3}}=\) (e) \(\frac{\left(-3.61 \times 10^{-4}\right)+\sqrt{\left(3.61 \times 10^{-4}\right)^{2}+4(1.00)\left(1.9 \times 10^{-5}\right)}}{2 \times(1.00)}\) [Hint: The significant figure rule for the extraction of a root is the same as for multiplication.]

The highest temperature of the following group is (a) \(217 \mathrm{K} ;\) (b) \(273 \mathrm{K} ;\) (c) \(217^{\circ} \mathrm{F} ;\) (d) \(105^{\circ} \mathrm{C} ;\) (e) \(373 \mathrm{K}\).
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