Chapter 1, Problem 142QP

The average blood volume in the human body in about 4.8 L. Convert this volume to the following units:

$\begin{array}{l}\left(\text{a}\right)\text{milliliters}\text{(mL)}\\ \left(\text{b}\right)\text{cublic}\text{centimeters}\text{}{\text{(cm}}^{\text{3}}\text{)}\\ \left(\text{c}\right)\text{cubic}\text{meters}{\text{(m}}^{\text{3}}\text{)}\end{array}$

Interpretation Introduction

Interpretation:

The conversion of volume $4.8\text{ L}$ into $\text{mL}$ .

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 $\text{L}$ into $\text{mL}$ is shown below:

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

$4.8\text{ L}$ is converted into $\text{mL}$ using conversion factor as shown below.

$\begin{array}{c}4.8\text{ L}=4.8\text{ L}\times \frac{1\text{ mL}}{{10}^{-3}\text{L}}\\ =4800\text{ L}\\ =4.8\times {10}^3\text{ mL}\end{array}$

The given volume has two significant figures that means that the answer will be reported in two significant figures.

Therefore, the final answer is $4.8\times {10}^3\text{ mL}$ .

Interpretation Introduction

Interpretation:

The conversion of volume $4.8\times {10}^3\text{ mL}$ into ${\text{cm}}^3$ .

Explanation of Solution

The relation between milliliter $\left(\text{mL}\right)$ and a cubic centimeter $\left({\text{cm}}^3\right)$ is shown below:

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

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

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

$4.8\times {10}^3\text{ mL}$ is converted into ${\text{cm}}^3$ using conversion factor as shown below.

$\begin{array}{c}4.8\times {10}^3\text{ mL}=4.8\times {10}^3\text{ mL}\times \frac{1{\text{ cm}}^3}{1\text{ mL}}\\ =4.8\times {10}^3{\text{ cm}}^3\end{array}$

The volume $4.8\times {10}^3\text{ mL}$ has two significant figures that means that the answer will be reported up to two significant figures. Therefore, the answer is $4.8\times {10}^3{\text{ cm}}^3$ .

Interpretation Introduction

Interpretation:

The conversion of volume $4.8\times {10}^3{\text{ cm}}^3$ into ${\text{m}}^3$ .

Explanation of Solution

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

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

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

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

$4.8\times {10}^3{\text{ cm}}^3$ is converted into ${\text{m}}^3$ using conversion factor as shown below.

$\begin{array}{c}4.8\times {10}^3{\text{ cm}}^3=4.8\times {10}^3{\text{ cm}}^3\times \frac{1\text{ m}}{100\text{ cm}}\times \frac{1\text{ m}}{100\text{ cm}}\times \frac{1\text{ m}}{100\text{ cm}}\\ =4.8\times {10}^3\times {10}^{-6}{\text{ m}}^3\\ =4.8\times {10}^{\left(3+\left(-6\right)\right)}{\text{ m}}^3\\ =4.8\times {10}^{-3}{\text{ m}}^3\end{array}$

The volume has two significant figures that means that the answer will be reported in two significant figures.

Therefore, the final answer up to two significant figures is $4.8\times {10}^{-3}{\text{ m}}^3$ .