Chapter 1, Problem 23QP

Carry out the following conversions. Report your answers to the correct number of signi�cant �gures.

(a) 375 m/s to ft/min

(b) 24.5 ${\text{cm}}^{\text{3}}$ to ${\text{in}}^{\text{3}}$

(c) 19.3 g/mL to lb/ ${\text{in}}^{\text{3}}$

Interpretation Introduction

Interpretation:

The conversion of $375\text{ m}/\text{s}$ to $\text{ft}/\text{min}$ .

Explanation of Solution

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

$0.9144\text{ m}=1\text{ yd}$

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

$1=\frac{1\text{ yd}}{\text{0}\text{.9144 m}}$

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

$1\text{ yd}=3\text{ ft}$

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

$1=\frac{3\text{ ft}}{1\text{ yd}}$

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 $\text{min}$ are shown below:

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

The $375\text{ m}/\text{s}$ is converted into $\text{ft/min}$ using the conversion factor as follows:

$\begin{array}{c}375\text{ m}/\text{s}=\frac{375\text{ m}}{1\text{ s}}\times \frac{1\text{ yd}}{\text{0}\text{.9144 m}}\times \frac{3\text{ ft}}{1\text{ yd}}\times \frac{60\text{ s}}{1\text{ min}}\\ =73818.8\text{ ft}/\text{min}\end{array}$

Therefore, $375\text{ m}/\text{s}$ is equal to $73818.8\text{ ft}/\text{min}$ . According to the rules of counting significant figures, the answer is $7.38\times {10}^4\text{ ft}/\text{min}$ .

Interpretation Introduction

Interpretation:

The conversion of $\text{24}{\text{.5 cm}}^3$ to ${\text{in}}^3$ .

Explanation of Solution

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

$1{\text{ in}}^3=16.387{\text{ cm}}^3$

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

$1=\frac{1{\text{ in}}^3}{16.387{\text{ cm}}^3}$

The $\text{24}{\text{.5 cm}}^3$ is converted into ${\text{in}}^3$ using the conversion factor as follows:

$\begin{array}{c}\text{24}{\text{.5 cm}}^3=\text{24}{\text{.5 cm}}^3\times \left(\frac{1{\text{ in}}^3}{16.387{\text{ cm}}^3}\right)\\ =1.49{\text{ in}}^3\end{array}$

Therefore, $\text{24}{\text{.5 cm}}^3$ is equal to $1.49{\text{ in}}^3$ . According to the rules of counting significant figures, the answer is rounded off to $1.50{\text{ in}}^3$ . The answer is $1.50{\text{ in}}^3$ .

Interpretation Introduction

Interpretation:

The conversion of $\text{19}\text{.3 g}/\text{mL}$ to $\text{lb}/{\text{in}}^3$ .

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 $\text{lb}$ are shown below:

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

The relation between $\text{mL}$ and ${\text{cm}}^3$ is shown below:

$1\text{ mL}=1{\text{ cm}}^3$

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

$1=\frac{1{\text{ cm}}^3}{1\text{ mL}}$

The relation between ${\text{in}}^3$ and ${\text{cm}}^3$ is shown below:

$1{\text{ in}}^3=16.387{\text{ cm}}^{\text{3}}$

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

$1=\frac{1{\text{ in}}^3}{16.387{\text{ cm}}^3}$

The $\text{19}\text{.3 g}/\text{mL}$ is converted into $\text{lb}/{\text{in}}^3$ using the conversion factor as follows:

$\begin{array}{c}\text{19}\text{.3 g}/\text{mL}=\frac{\text{19}\text{.3 g}}{1\text{ mL}}\times \frac{1\text{ lb}}{\text{453}\text{.6 g}}\times \frac{\text{1 mL}}{1{\text{ cm}}^3}\times \frac{16.387{\text{ cm}}^3}{1{\text{ in}}^3}\\ =0.697\text{ lb}/{\text{in}}^3\end{array}$

Therefore, $\text{19}\text{.3 g}/\text{mL}$ is equal to $0.697\text{ lb}/{\text{in}}^3$ . According to the rules of counting significant figures, the answer is $0.697\text{ lb}/{\text{in}}^3$ .