Chapter 3, Problem 74A

a)

Interpretation Introduction

Interpretation : The unit of centiseconds to seconds is to be converted.

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

Answer to Problem 74A

The unit of centiseconds to seconds is $1.57\text{s}$ .

Explanation of Solution

Given information :

The given value is $157\text{cs}$ .

It is known that $\text{1}\text{s}\text{=}{10}^2\text{cs}$ .

An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

The desired conversion is $\text{cs}\to \text{s}$ .

The conversion of the units is given as

  $\begin{array}{c}157\text{cs}=157\cancel{\text{cs}}\times \frac{{10}^{-2}\text{s}}{1\cancel{\text{cs}}}\left(\because \text{1}\text{s}\text{=}{10}^2\text{cs}\right)\\ =1.57\text{s}\end{array}$

b)

Interpretation Introduction

Interpretation : The units of liters to milliliters are to be converted.

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

Answer to Problem 74A

The units of liters to milliliters are $4.27\times {10}^4\text{mL}$ .

Explanation of Solution

Given information :

The given value is $42.7\text{L}$ .

It is known that $\text{1}\text{L}\text{=}{\text{10}}^3\text{mL}$ .

An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

The desired conversion is $\text{L}\to \text{mL}$ .

The conversion of the expression is given as

  $\begin{array}{c}42.7\text{L}\text{=}42.7\cancel{\text{L}}\times \frac{{10}^3\text{mL}}{1\cancel{\text{L}}}\left(\because \text{1}\text{L}\text{=}{\text{10}}^3\text{mL}\right)\\ \text{=}\text{4}\text{.27}\times {10}^4\text{mL}\end{array}$

c)

Interpretation Introduction

Interpretation : The unit of nanometers to millimeters is to be converted.

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

Answer to Problem 74A

The unit of nanometers to millimeters is $2.61\times {10}^{-4}\text{mm}$ .

Explanation of Solution

Given information :

The given value is $261\text{nm}$ .

It is known that $\text{1}\text{m}\text{=}{10}^9\text{nm}$ and $\text{1}\text{m}\text{=}{10}^3\text{mm}$ .

An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

The desired conversion is $\text{nm}\to \text{mm}$ .

The conversion of the units is given as

  $\begin{array}{c}261\text{nm}=261\cancel{\text{nm}}\times \frac{{10}^{-9}\cancel{\text{m}}}{1\cancel{\text{nm}}}\times \frac{{10}^3\text{mm}}{1\cancel{\text{m}}}\left(\because \text{1}\text{m}\text{=}{10}^9\text{nm},\text{1}\text{m}\text{=}{10}^3\text{mm}\right)\\ =261\times {10}^{-6}\text{mm}\\ =2.61\times {10}^{-4}\text{mm}\end{array}$

d)

Interpretation Introduction

Interpretation : The units of kilometer to decimeter are to be converted.

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

Answer to Problem 74A

The units of kilometer to decimeter are $6.5\times {10}^2\text{dm}$ .

Explanation of Solution

Given information :

The given value is $0.0065\text{km}$ .

It is known that $\text{1}\text{km}\text{=}{\text{10}}^3\text{m}$ and $\text{1}\text{m}\text{=}{\text{10}}^1\text{dm}$ .

An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

The desired conversion is $\text{km}\to \text{dm}$ .

The conversion of the expression is given as

  $\begin{array}{c}0.0065\text{km}\text{=}0.0065\cancel{\text{km}}\times \frac{{10}^3\cancel{\text{m}}}{1\cancel{\text{km}}}\times \frac{10\text{dm}}{1\cancel{\text{m}}}\left(\because \text{1}\text{km}\text{=}{\text{10}}^3\text{m},\text{1}\text{m}\text{=}{\text{10}}^1\text{dm}\right)\\ =0.0065\times {10}^4\text{dm}\\ \text{=}6.5\times {10}^2\text{dm}\end{array}$

e)

Interpretation Introduction

Interpretation : The units of centigrams to kilograms is to be converted.

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

Answer to Problem 74A

The units of centigrams to kilograms are $6.42\times {10}^{-3}\text{kg}$ .

Explanation of Solution

Given information :

The given value is $642\text{cg}$ .

It is known that $\text{1}\text{kg}\text{=}{\text{10}}^3\text{g}$ and $\text{1}\text{g}\text{=}{\text{10}}^2\text{cg}$ .

An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

The desired conversion is $\text{cg}\to \text{kg}$ .

The conversion of the expression is given as

  $\begin{array}{c}642\text{cg}\text{=}642\cancel{\text{cg}}\times \frac{{10}^{-2}\cancel{\text{g}}}{\cancel{\text{cg}}}\times \frac{{10}^{-3}\text{kg}}{1\cancel{\text{g}}}\left(\because \text{1}\text{kg}\text{=}{\text{10}}^3\text{g,}\text{1}\text{g}\text{=}{\text{10}}^2\text{cg}\right)\\ =642\times {10}^{-5}\text{kg}\\ \text{=}642\times {10}^{-3}\text{kg}\end{array}$

f)

Interpretation Introduction

Interpretation : The units of centigrams to nanograms is to be converted.

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

Answer to Problem 74A

The units of centigrams to nanograms are $8.25\times {\text{10}}^9\text{ng}$ .

Explanation of Solution

Given information :

The given value is $8.25\times {\text{10}}^2\text{cg}$ .

It is known that $\text{1}\text{g}\text{=}{\text{10}}^2\text{cg}$ and $\text{1}\text{g}\text{=}{\text{10}}^9\text{ng}$ .

An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

The desired conversion is $\text{cg}\to \text{ng}$ .

The conversion of the expression is given as

  $\begin{array}{c}8.25\times {\text{10}}^2\text{cg}\text{=}8.25\times {\text{10}}^2\cancel{\text{cg}}\times \frac{{10}^{-2}\cancel{\text{g}}}{1\cancel{\text{cg}}}\times \frac{{10}^9\text{ng}}{1\cancel{\text{g}}}\left(\because \text{1}\text{g}\text{=}{\text{10}}^2\text{cg},\text{1}\text{g}\text{=}{\text{10}}^9\text{ng}\right)\\ =8.25\times {\text{10}}^9\text{ng}\end{array}$