Chapter 8, Problem 97A

(a)

Interpretation Introduction

Interpretation: The given value in millimeters needs to be converted into micrometers.

Concept Introduction: The conversion factor is used to convert one set of units into other by simply multiplying and dividing with numbers.

The following conversion factors can be used in the given problem:

  $1\text{ mm}={10}^{-3}\text{ m}$

And,

  $1\mu \text{m}={10}^{-6}\text{ m}$

Here, $\mu \text{m}$ is micrometers.

Explanation of Solution

The given value is 66.5 mm. To convert this value into micrometers, the following conversion factors can be used:

  $\frac{{10}^{-3}\text{ m}}{1\text{ mm}}$ and, $\frac{1\mu \text{m}}{{10}^{-6}\text{ m}}$

The conversion can be shown as follows:

  $\begin{array}{c}66.5\cancel{\text{mm}}\left(\frac{{10}^{-3}\cancel{\text{m}}}{1\cancel{\text{mm}}}\right)\left(\frac{1\mu \text{m}}{{10}^{-6}\cancel{\text{m}}}\right)=66.5\times {10}^{-3+6}\mu \text{m}\\ =66.5\times {10}^3\mu \text{m}\\ =6.65\times {10}^4\mu \text{m}\end{array}$

Thus, the final value after conversion will be $6.65\times {10}^4\mu \text{m}$ .

(b)

Interpretation Introduction

Interpretation: The given value in grams needs to be converted into centigrams.

Concept Introduction: The conversion factor is used to convert one set of units into other by simply multiplying and dividing with numbers.

The following conversion factor can be used in the given problem:

  $1\text{ g}={10}^2\text{ cg}$

Here, $\text{cg}$ is centigrams.

Explanation of Solution

The given value is $4\times {10}^{-2}\text{ g}$ . To convert this value into centigrams, the following conversion factor can be used:

  $\frac{{10}^2\text{ cg}}{1\text{ g}}$

The conversion can be shown as follows:

  $\begin{array}{c}4\times {10}^{-2}\cancel{\text{g}}\left(\frac{{10}^2\text{ cg}}{1\cancel{\text{g}}}\right)=4\times {10}^{-2+2}\text{ cg}\\ =4\times {10}^0\text{ cg}\\ =4\text{ cg}\end{array}$

Thus, the final value after conversion will be $4\text{ cg}$ .

(c)

Interpretation Introduction

Interpretation: The given value in milligrams per milliliter needs to be converted into decigrams per liter.

Concept Introduction: The conversion factor is used to convert one set of units into other by simply multiplying and dividing with numbers.

Explanation of Solution

The following conversion factors can be used in the given problem:

  $1\text{ mg}={10}^{-3}\text{ g}$

  $1\text{ dg}={10}^{-1}\text{ g}$

And,

  $1\text{ mL}={10}^{-3}\text{ L}$

Here, $\text{dg}$ is the decigram.

The given value is 5.62 mg/mL. To convert this value into decigrams per liter, the following conversion factors can be used:

  $\frac{{10}^{-3}\text{ g}}{1\text{ mg}}$ , $\frac{1\text{ dg}}{{10}^{-1}\text{ g}}$ and, $\frac{1\text{ mL}}{{10}^{-3}\text{ L}}$

The conversion can be shown as follows:

  $\begin{array}{c}5.62\frac{\cancel{\text{mg}}}{\cancel{\text{mL}}}\left(\frac{{10}^{-3}\cancel{\text{g}}}{1\cancel{\text{mg}}}\right)\left(\frac{1\text{ dg}}{{10}^{-1}\cancel{\text{g}}}\right)\left(\frac{1\cancel{\text{mL}}}{{10}^{-3}\text{ L}}\right)=5.62\times {10}^{-3+1+3}\text{ dg/L}\\ =5.62\times {10}^1\text{ dg/L}\\ =56.2\text{ dg/L}\end{array}$

Thus, the final value after conversion will be $56.2\text{ dg/L}$ .

(d)

Interpretation Introduction

Interpretation: The given value in kilometers per hour needs to be converted into a meter per second.

Concept Introduction: The conversion factor is used to convert one set of units into other by simply multiplying and dividing with numbers.

Explanation of Solution

The following conversion factors can be used in the given problem:

  $1\text{ km}={10}^3\text{ m}$

And,

  $\begin{array}{l}1\text{ h}=60\text{ min}\\ \text{1 min}=60\text{ s}\end{array}$

Here, min represents minutes.

The given value is 85 km/h. To convert this value into meters per second, the following conversion factors can be used:

  $\frac{{10}^3\text{ m}}{1\text{ km}}$ , $\frac{1\text{ h}}{60\text{ min}}$ and, $\frac{1\text{ min}}{\text{60 s}}$

The conversion can be shown as follows:

  $\begin{array}{c}85\frac{\cancel{\text{km}}}{\cancel{\text{h}}}\left(\frac{{10}^3\text{ m}}{1\cancel{\text{km}}}\right)\left(\frac{1\cancel{\text{h}}}{60\cancel{\min }}\right)\left(\frac{1\cancel{\min }}{\text{60 s}}\right)=\frac{85\times {10}^3}{60\times 60}\text{ m/s}\\ =23.61\text{ m/s}\end{array}$

Thus, the final value after conversion will be $23.61\text{ m/s}$ .