Chapter 3.3, Problem 53LC

a)

Interpretation Introduction

Interpretation : The value $14.8\text{ g}$ is to be converted into $\text{μg}$ .

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. Dimensional analysis is a useful method for resolving conversion problems where measurements in one unit are changed to equal measurements.

Answer to Problem 53LC

  $1.48\times {10}^7\text{μg}$ .

Explanation of Solution

Given information :

The given value is $14.8\text{g}$ .

It is known that $\text{1}\text{g}\text{=}{10}^6\text{μg}$ .

The desired conversion is $\text{g}\to \text{μg}$ .

The conversion of the units is given as:

  $\begin{array}{c}14.8\text{g}=14.8\cancel{\text{g}}\times \frac{{10}^6\text{μg}}{1\cancel{\text{g}}}\left(\because \text{1}\text{g}\text{=}{10}^6\text{μg}\right)\\ =14.8\times {10}^6\text{μg}\\ =1.48\times {10}^7\text{μg}\end{array}$

b)

Interpretation Introduction

Interpretation : The value $3.72\text{ g}$ is to be converted into $\text{μg}$ .

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. Dimensional analysis is a useful method for resolving conversion problems where measurements in one unit are changed to equal measurements.

Answer to Problem 53LC

  $3.72\times {10}^{-3}\text{kg}$ .

Explanation of Solution

Given information :

The given value is $3.72\text{g}$ .

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

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

The conversion of the expression is given as:

  $\begin{array}{c}3.72\text{g}\text{=3}\text{.72}\cancel{\text{g}}\times \frac{{10}^{-3}\text{kg}}{1\cancel{\text{g}}}\left(\because \text{1}\text{kg}\text{=}{\text{10}}^3\text{g}\right)\\ \text{=3}\text{.72}\times {10}^{-3}\text{kg}\end{array}$

c)

Interpretation Introduction

Interpretation : The value $66.3\text{ L}$ is to be converted into ${\text{cm}}^{\text{3}}$ .

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. Dimensional analysis is a useful method for resolving conversion problems where measurements in one unit are changed to equal measurements.

Answer to Problem 53LC

  $6.63\times {10}^4{\text{cm}}^3$ .

Explanation of Solution

Given information :

The given value is $66.3\text{L}$ .

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

The desired conversion is $\text{L}\to {\text{cm}}^3$ .

The conversion of the units is given as:

  $\begin{array}{c}66.3\text{L}=66.3\cancel{\text{L}}\times \frac{{10}^3{\text{cm}}^3}{1\cancel{\text{L}}}\left(\because \text{1}\text{L}\text{=}{10}^3{\text{cm}}^3\right)\\ =66.3\times {10}^3{\text{cm}}^3\\ =6.63\times {10}^4{\text{cm}}^3\end{array}$

d)

Interpretation Introduction

Interpretation : The value $7.5\times {10}^4\text{ J}$ is to be converted into $\text{kJ}$ .

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. Dimensional analysis is a useful method for resolving conversion problems where measurements in one unit are changed to equal measurements.

Answer to Problem 53LC

  $7.5\times {10}^1\text{kJ}$ .

Explanation of Solution

Given information :

The given value is $7.5\times {10}^4\text{J}$ .

It is known that $\text{1}\text{kJ}\text{=}{\text{10}}^3\text{J}$ .

The desired conversion is $\text{J}\to \text{kJ}$ .

The conversion of the expression is given as

  $\begin{array}{c}7.5\times {10}^4\text{J}\text{=}7.5\times {10}^4\cancel{\text{J}}\times \frac{{10}^{-3}\text{kJ}}{1\cancel{\text{J}}}\left(\because \text{1}\text{kJ}\text{=}{\text{10}}^3\text{J}\right)\\ =7.5\times {10}^1\text{kJ}\end{array}$

e)

Interpretation Introduction

Interpretation : The value $3.9\times {10}^5\text{ mg}$ is to be converted into $\text{dg}$ .

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. Dimensional analysis is a useful method for resolving conversion problems where measurements in one unit are changed to equal measurements.

Answer to Problem 53LC

  $3.9\times {10}^3\text{dg}$ .

Explanation of Solution

Given information :

The given value is $3.9\times {10}^5\text{mg}$ .

It is known that $\text{1}\text{g}\text{=}{\text{10}}^3\text{mg}$ and $\text{1}\text{g}\text{=}{\text{10}}^1\text{dg}$ .

The desired conversion is $\text{mg}\to \text{dg}$ .

The conversion of the expression is given as

  $\begin{array}{c}3.9\times {10}^5\text{mg}\text{=}3.9\times {10}^5\cancel{\text{mg}}\times \frac{{10}^{-3}\cancel{\text{g}}}{\cancel{\text{mg}}}\times \frac{{10}^1\text{dg}}{1\cancel{\text{g}}}\left(\because \text{1}\text{g}\text{=}{\text{10}}^3\text{mg,}\text{1}\text{g}\text{=}{\text{10}}^1\text{dg}\right)\\ =3.9\times {10}^3\text{dg}\end{array}$

f)

Interpretation Introduction

Interpretation : The value $2.1\times {10}^{-4}\text{ dL}$ is to be converted into $\text{μL}$ .

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. Dimensional analysis is a useful method for resolving conversion problems where measurements in one unit are changed to equal measurements.

Answer to Problem 53LC

  $\text{2}\text{.1}\times {\text{10}}^1\text{μL}$ .

Explanation of Solution

Given information :

The given value is $\text{2}\text{.1}\times {\text{10}}^{-4}\text{dL}$ .

It is known that $\text{1}\text{L}\text{=}{\text{10}}^1\text{dL}$ and $\text{1}\text{L}\text{=}{\text{10}}^6\text{μL}$ .

The desired conversion is $\text{dL}\to \text{μL}$ .

The conversion of the expression is given as

  $\begin{array}{c}\text{2}\text{.1}\times {\text{10}}^{-4}\text{dL}\text{= 2}\text{.1}\times {\text{10}}^{-4}\cancel{\text{dL}}\times \frac{{10}^{-1}\cancel{\text{L}}}{1\cancel{\text{dL}}}\times \frac{{10}^6\text{μL}}{1\cancel{\text{L}}}\left(\because \text{1}\text{L}\text{=}{\text{10}}^1\text{dL},\text{1}\text{L}\text{=}{\text{10}}^6\text{μL}\right)\\ =\text{2}\text{.1}\times {\text{10}}^1\text{μL}\end{array}$