Chapter 3.3, Problem 42SP

Interpretation Introduction

Interpretation : The expression of $15{\text{cm}}^3$ to litres is to be converted.

Concept Introduction : A conversion factor is a ratio of equivalent measurements. Dimensional analysis is a useful method for resolving conversion problems where measurements in one unit are changed to equal measurements in another.

Answer to Problem 42SP

The expression of $15{\text{cm}}^3$ is $1.5\times {10}^{-2}\text{L}$ .

Explanation of Solution

Given information :

The given expression is $15{\text{cm}}^3$ .

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

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 ${\text{cm}}^3\to \text{L}$ .

The conversion of the expression is given as

  $\begin{array}{c}15{\text{cm}}^3\text{=}15\cancel{{\text{cm}}^3}\times \frac{{10}^{-3}\text{L}}{1\cancel{{\text{cm}}^3}}\left(\because \text{1}\text{L}\text{=}{\text{10}}^3{\text{cm}}^3\right)\\ =1.5\times {10}^{-2}\text{L}\end{array}$

Interpretation Introduction

Interpretation : The expression of $7.38\text{g}$ to kilograms is to be converted.

Concept Introduction : A conversion factor is a ratio of equivalent measurements. Dimensional analysis is a useful method for resolving conversion problems where measurements in one unit are changed to equal measurements in another.

Answer to Problem 42SP

The expression of $7.38\text{g}$ is $7.38\times {10}^{-3}\text{kg}$ .

Explanation of Solution

Given information :

The given expression is $7.38\text{g}$ .

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

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 $\text{g}\to \text{kg}$ .

The conversion of the expression is given as

  $\begin{array}{c}7.38\text{g}\text{=}7.38\cancel{\text{g}}\times \frac{{10}^{-3}\text{kg}}{1\cancel{\text{g}}}\left(\because \text{1}\text{kg}\text{=}{\text{10}}^3\text{g}\right)\\ =7.38\times {10}^{-3}\text{kg}\end{array}$

Interpretation Introduction

Interpretation : The expression of $6.7\text{s}$ to millisecond is to be converted.

Concept Introduction : A conversion factor is a ratio of equivalent measurements. Dimensional analysis is a useful method for resolving conversion problems where measurements in one unit are changed to equal measurements in another.

Answer to Problem 42SP

The expression of $6.7\text{s}$ is $\text{6}{\text{.7×10}}^{\text{3}}\text{ms}$ .

Explanation of Solution

Given information :

The given expression is $6.7\text{s}$ .

It is known that $\text{1}\text{s}\text{=}{\text{10}}^3\text{ms}$ .

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 $\text{s}\to \text{ms}$ .

The conversion of the expression is given as

  $\begin{array}{c}6.7\text{s}\text{=}6.7\cancel{\text{s}}\times \frac{{10}^3\text{ms}}{1\cancel{\text{s}}}\left(\because \text{1}\text{s}\text{=}{\text{10}}^3\text{ms}\right)\\ =6.7\times {10}^3\text{ms}\end{array}$

Interpretation Introduction

Interpretation : The expression of $94.5\text{g}$ to micrograms is to be converted.

Concept Introduction : A conversion factor is a ratio of equivalent measurements. Dimensional analysis is a useful method for resolving conversion problems where measurements in one unit are changed to equal measurements in another.

Answer to Problem 42SP

The expression of $94.5\text{g}$ is $\text{9}{\text{.45×10}}^{\text{7}}\text{μg}$ .

Explanation of Solution

Given information :

The given expression is $94.5\text{g}$ .

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

A conversion factor is a ratio of equivalent measurements. Dimensional analysis is a useful method for resolving conversion problems where measurements in one unit are changed to equal measurements in another.

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

The conversion of the expression is given as

  $\begin{array}{c}94.5\text{g}\text{=}94.5\cancel{\text{g}}\times \frac{{10}^6\text{μg}}{1\cancel{\text{g}}}\left(\because \text{1}\text{g}\text{=}{\text{10}}^{\text{6}}\text{μg}\right)\\ =9.45\times {10}^7\text{μg}\end{array}$