Chapter 1, Problem 24QP

(a)

Interpretation Introduction

Interpretation:

The conversion of $27\text{ ft}/\text{s}$ to $\text{cm}/\text{min}$ .

Explanation of Solution

The relation between Foot $\left(\text{ft}\right)$ and $\text{in}$ is shown below:

$1\text{ ft}=12\text{ in}$

The conversion factors used to convert $\text{ft}$ into $\text{in}$ is shown below:

$\frac{1\text{ ft}}{12\text{ in}}\text{or}\frac{12\text{ in}}{1\text{ ft}}$

The relation between $\text{in}$ and $\text{cm}$ is shown below:

$1\text{ in}=2.54\text{ cm}$

The conversion factors used to convert $\text{yd}$ into $\text{ft}$ is shown below:

$\frac{1\text{ in}}{\text{2}\text{.54 cm}}\text{or}\frac{\text{2}\text{.54 cm}}{1\text{ in}}$

The relation between $\text{min}$ and $\text{s}$ is shown below:

$1\text{ min}=60\text{ s}$

The conversion factors used to convert $\text{s}$ into $\text{min}$ is shown below:

$\frac{1\text{ min}}{60\text{ s}}\text{or}\frac{60\text{ s}}{1\text{ min}}$

The $27\text{ ft}/\text{s}$ is converted into $\text{cm}/\text{min}$ using the conversion factor as follows:

$\begin{array}{c}27\text{ ft}/\text{s}=\frac{27\text{ ft}}{1\text{ s}}\times \frac{12\text{ in}}{1\text{ ft}}\times \frac{2.54\text{ cm}}{1\text{ in}}\times \frac{60\text{ s}}{1\text{ min}}\\ =49377.6\text{ cm}/\text{min}\end{array}$

Therefore, $27\text{ ft}/\text{s}$ is equal to $49377.6\text{ cm}/\text{min}$ . According to the rules of counting significant figures, $27\text{ ft}/\text{s}$ has two significant figures. Therefore, the answer is $4.9\times {10}^4\text{ cm}/\text{min}$ .

(b)

Interpretation Introduction

Interpretation:

The conversion of ${\text{2764 ft}}^3$ to ${\text{m}}^3$ .

Explanation of Solution

The relation between Foot $\left(\text{ft}\right)$ and $\text{m}$ is shown below:

$3\text{ ft}=0.9144\text{ m}$

The conversion factors used to convert ${\text{cm}}^3$ into ${\text{m}}^3$ is shown below:

$\frac{3\text{ ft}}{\text{0}\text{.9144 m}}\text{or}\frac{\text{0}\text{.9144 m}}{\text{3 ft}}$

The ${\text{2764 ft}}^3$ is converted into ${\text{m}}^3$ using the conversion factor as follows:

$\begin{array}{c}{\text{2764 ft}}^3={\text{2764 ft}}^3\times {\left(\frac{0.9144\text{ m}}{3\text{ ft}}\right)}^3\\ =78.267{\text{ m}}^3\end{array}$

Therefore, ${\text{2764 ft}}^3$ is equal to $78.267{\text{ m}}^3$ . The given number ${\text{2764 ft}}^3$ has four significant figures. As a result, the final answer will be rounded off to four significant figures. Therefore, the final answer is $78.27{\text{ m}}^3$ .

(c)

Interpretation Introduction

Interpretation:

The conversion of $\text{0}\text{.927 g}/\text{mL}$ to $\text{lb}/\text{gal}$ .

Explanation of Solution

The relation between $\text{g}$ and Pound $\left(\text{lb}\right)$ is shown below:

$1\text{ lb}=453.6\text{ g}$

The conversion factors used to convert $\text{g}$ into $\text{lb}$ is shown below:

$\frac{1\text{ lb}}{\text{453}\text{.6 g}}\text{or}\frac{\text{453}\text{.6 g}}{1\text{ lb}}$

The relation between $\text{mL}$ and $\text{L}$ is shown below:

$1\text{ L}=1000\text{ mL}$

The conversion factors used to convert $\text{mL}$ into $\text{L}$ is shown below:

$\frac{1\text{ L}}{1000\text{ mL}}\text{or}\frac{1000\text{ mL}}{1\text{ L}}$

The relation between $\text{L}$ and $\text{gal}$ is shown below:

$1\text{ gal}=3.785\text{ L}$

The conversion factors used to convert $\text{L}$ into $\text{gal}$ is shown below:

$\frac{1\text{ gal}}{2.785\text{ L}}\text{or}\frac{2.785\text{ L}}{1\text{ gal}}$

The $\text{0}\text{.927 g}/\text{mL}$ is converted into $\text{lb}/\text{gal}$ using the conversion factor as follows:

$\begin{array}{c}\text{0}\text{.927 g}/\text{mL}=\frac{\text{0}\text{.927 g }}{1\text{ mL}}\times \frac{1\text{ lb}}{\text{453}\text{.6 g}}\times \frac{\text{1000 mL}}{1\text{ L}}\times \frac{3.785\text{ L}}{1\text{ gal}}\\ =7.735\text{ lb}/\text{gal}\end{array}$

Therefore, $\text{0}\text{.927 g}/\text{mL}$ is equal to $7.735\text{ lb}/\text{gal}$ . The given number $\text{0}\text{.927 g}/\text{mL}$ has three significant figures. As a result, the final answer will be rounded off to three significant figures. Therefore, the final answer is $7.74\text{ lb}/\text{gal}$ .