Chapter 1, Problem 19QP

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

(a) 36 mm to m

(b) 357 kg to g

(c) 76.50 mL to L

(d) 0.0084670 m to cm

(e) 597 nm to m

(f) 36.5 in to cm

(g) 168 lb to g

(h) 914 qt to L

(i) 44.5 cm to in

(j) 236.504 g to lb

(k) 2.0 L to qt

Interpretation Introduction

Interpretation:

The conversion of $36\text{ mm}$ to $\text{m}$ .

Explanation of Solution

The relation between millimeter $\left(\text{mm}\right)$ and meter $\left(\text{m}\right)$ is shown below:

$1\text{ mm}={10}^{-3}\text{ m}$

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

$\frac{1\text{ mm}}{{\text{10}}^{-3}\text{ m}}\text{or}\frac{{\text{10}}^{-3}\text{ m}}{1\text{ mm}}$

$36\text{ mm}$ is converted into $\text{m}$ using the conversion factor as follows:

$\begin{array}{c}36\text{ mm}=36\text{ mm}\times \frac{{10}^{-3}\text{ m}}{1\text{ mm}}\\ =0.036\text{ m}\end{array}$

The given number $36\text{ mm}$ has two significant figures. Therefore, the answer will be reported in two significant figures.

The final answer is $0.036\text{ m}$ .

Interpretation Introduction

Interpretation:

The conversion of $357\text{ kg}$ to $\text{g}$ .

Explanation of Solution

The relation between kilogram $\left(\text{kg}\right)$ and gram $\left(\text{g}\right)$ is shown below:

$1\text{ kg}=\text{1000 g}$

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

$\frac{1\text{ kg}}{1000\text{ g}}\text{or}\frac{1000\text{ g}}{1\text{ kg}}$

$357\text{ kg}$ is converted into $\text{g}$ using conversion factor as shown below.

$\begin{array}{c}357\text{ kg}=357\text{ kg}\times \frac{1000\text{ g}}{1\text{ kg}}\\ =357000\text{ g}\\ =3.57\times {10}^5\text{g}\end{array}$

The given number $357\text{ kg}$ has three significant figures. Therefore, the answer will be reported in three significant figures.

Therefore, the final answer is $3.57\times {10}^5\text{g}$ .

Interpretation Introduction

Interpretation:

The conversion of $76.50\text{ mL}$ to $\text{L}$ .

Explanation of Solution

The relation between milliliter $\left(\text{mL}\right)$ and liter $\left(\text{L}\right)$ is shown below:

$1\text{ mL}={10}^{-3}\text{L}$

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

$\frac{1\text{ mL}}{{10}^{-3}\text{L}}\text{or}\frac{{10}^{-3}\text{L}}{1\text{ mL}}$

$76.50\text{ mL}$ is converted into $\text{L}$ using conversion factor is shown below.

$\begin{array}{c}76.50\text{ mL}=76.50\text{ mL}\times \frac{{10}^{-3}\text{ L}}{1\text{ mL}}\\ =0.07650\text{ L}\end{array}$

The given number $76.50\text{ mL}$ has four significant figures that means that the answer will be reported in four significant figures also.

Therefore, the final answer is $0.07650\text{ L}$ .

Interpretation Introduction

Interpretation:

The conversion of $0.0084670\text{ m}$ to $\text{cm}$ .

Explanation of Solution

The relation between meter $\left(\text{m}\right)$ and centimeter $\left(\text{cm}\right)$ is shown below:

$1\text{ m}=100\text{ cm}$

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

$\frac{1\text{ m}}{100\text{ cm}}\text{or}\frac{100\text{ cm}}{1\text{ m}}$

$0.0084670\text{ m}$ is converted into $\text{cm}$ using conversion factor is shown below.

$\begin{array}{c}0.0084670\text{ m}=0.0084670\text{ m}\times \frac{\text{100 cm}}{1\text{ m}}\\ =0.84670\text{ cm}\end{array}$

The given number $0.0084670\text{ m}$ has five significant figures that means that the answer will be reported in five significant figures only.

Therefore, the final answer is $0.84670\text{ cm}$ .

Interpretation Introduction

Interpretation:

The conversion of $\text{597 nm}$ to $\text{m}$ .

Explanation of Solution

The relation between nanometer $\left(\text{nm}\right)$ and meter $\left(\text{m}\right)$ is shown below:

$1\text{ mm}={10}^{-9}\text{ m}$

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

$\frac{1\text{ nm}}{{\text{10}}^{-9}\text{ m}}\text{or}\frac{{\text{10}}^{-9}\text{ m}}{1\text{ nm}}$

$\text{597 nm}$ is converted into $\text{m}$ using the conversion factor as follows:

$\begin{array}{c}\text{597 nm}=\text{597 nm}\times \frac{{10}^{-9}\text{ m}}{1\text{ nm}}\\ \text{=5}\text{.97}\times {10}^{-9}\times {10}^2\text{ m}\\ =\text{5}\text{.97}\times {10}^{\left(-9+2\right)}\text{ m}\\ =5.97\times {10}^{-7}\text{ m}\end{array}$

The given number $\text{597 nm}$ has three significant figures. Therefore, the answer will be reported in three significant figures only.

The final answer is $\text{5}\text{.97}\times {10}^{-7}\text{ m}$ .

Interpretation Introduction

Interpretation:

The conversion of $36.5\text{ in}$ to $\text{cm}$ .

Explanation of Solution

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

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

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

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

$36.5\text{ in}$ is converted into $\text{cm}$ using the conversion factor as follows:

$\begin{array}{c}36.5\text{ in}=36.5\text{ in}\times \frac{\text{2}\text{.54 cm}}{1\text{ in}}\\ =\text{92}\text{.7 cm}\end{array}$

The given number has three significant figures, hence, the answer will be reported in three significant figures only.

The final answer is $92.7\text{ cm}$ .

Interpretation Introduction

Interpretation:

The conversion of $168\text{ lb}$ to $\text{g}$ .

Explanation of Solution

The relation between $\text{lb}$ and $\text{g}$ is shown below:

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

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

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

$168\text{ lb}$ is converted into $\text{g}$ using the conversion factor as follows:

$\begin{array}{c}168\text{ lb}=168\text{ lb}\times \frac{\text{453}\text{.6 g}}{1\text{ lb}}\\ =76204.8\text{ g}\\ =\text{7}\text{.62}\times {10}^4\text{ g}\end{array}$

The given number has three significant figures, hence, the answer will be reported in three significant figures only.

The final answer up to three significant figures is $\text{7}\text{.62}\times {10}^4\text{ g}$ .

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Interpretation Introduction

Interpretation:

The conversion of $914\text{ qt}$ to $\text{L}$ .

Explanation of Solution

The relation between Quart $\left(\text{qt}\right)$ and Liter $\left(\text{L}\right)$ is shown below:

$1\text{ qt}=0.9464\text{ L}$

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

$\frac{1\text{ qt}}{0.9464\text{ L}}\text{or}\frac{0.9464\text{ L}}{1\text{ qt}}$

$914\text{ qt}$ is converted into $\text{L}$ using the conversion factor as follows:

$\begin{array}{c}914\text{ qt}=914\text{ qt}\times \frac{0.9464\text{ L}}{1\text{ qt}}\\ =865.0096\text{ L}\\ =865\text{ L}\end{array}$

The given number $914\text{ qt}$ has three significant figures that means that the answer will be reported in three significant figures only.

Therefore, the final answer is $865\text{ L}$ .

Interpretation Introduction

Interpretation:

The conversion of $44.5\text{ cm}$ to $\text{in}$ .

Explanation of Solution

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

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

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

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

$44.5\text{ cm}$ is converted into $\text{cm}$ using the conversion factor as follows:

$\begin{array}{c}44.5\text{ cm}=44.5\text{ cm}\times \frac{1\text{ in}}{\text{2}\text{.54 cm}}\\ =17.519\text{ in}\\ \text{=17}\text{.5 in}\end{array}$

The given number has three significant figures that means that the answer will be reported in three significant figures only.

Therefore, the final answer is $17.5\text{ in}$ .

Interpretation Introduction

Interpretation:

The conversion of $236.504\text{ g}$ to $\text{lb}$ .

Explanation of Solution

The relation between $\text{lb}$ and $\text{g}$ is shown below:

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

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

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

$236.504\text{ g}$ is converted into $\text{g}$ using the conversion factor as follows:

$\begin{array}{c}236.504\text{ g}=236.504\text{ g}\times \frac{1\text{ lb}}{\text{453}\text{.6 g}}\\ =0.5214\text{ lb}\\ =0.5214\text{ lb}\end{array}$

The final answer is $0.5214\text{ lb}$ .

Interpretation Introduction

Interpretation:

The conversion of $2.0\text{ L}$ to $\text{qt}$ .

Explanation of Solution

The relation between Quart $\left(\text{qt}\right)$ and Liter $\left(\text{L}\right)$ is shown below:

$1\text{ qt}=0.9464\text{ L}$

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

$\frac{1\text{ qt}}{0.9464\text{ L}}\text{or}\frac{0.9464\text{ L}}{1\text{ qt}}$

$2.0\text{ L}$ is converted into $\text{qt}$ using the conversion factor as follows:

$\begin{array}{c}2.0\text{ L}=2.0\text{ L}\times \frac{1\text{ qt}}{0.9464\text{ L}}\\ =2.11\text{ qt}\\ =2.1\text{ qt}\end{array}$

The given number has two significant figures that means thar the answer will be reported in two significant figures only.

Therefore, the final is $2.1\text{ qt}$ .