Chapter 3.3, Problem 52LC

Interpretation Introduction

Interpretation : The quantity given in minutes is to be converted into the hour.

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

Answer to Problem 52LC

The unit of minutes to an hour is $1.7\times {10}^{-2}\text{hr}$ .

Explanation of Solution

Given information :

The given unit is minutes.

It is known that $\text{1}\text{hr}\text{=}60\text{mins}$ .

The dimensional analysis is a technique used for the dimensions of the measurement or units to analyze and resolve problems.

The desired conversion is $\text{min}\to \text{hr}$ .

The conversion of the units is given as:

  $\begin{array}{c}\text{mins}=1\cancel{\min }\times \frac{1\text{hr}}{60\cancel{\min }}\left(\because \text{1}\text{hr}\text{=}60\text{mins}\right)\\ =0.017\text{hr}\\ =1.7\text{hr}\end{array}$

Interpretation Introduction

Interpretation : The quantity given in grams is to be converted into the milligrams.

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

Answer to Problem 52LC

The units of grams to milligrams are ${10}^3\text{mg}$ .

Explanation of Solution

Given information :

The given unit is grams.

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

The dimensional analysis is a technique used for the dimensions of the measurement or units to analyze and resolve problems.

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

The conversion of the expression is given as:

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

Interpretation Introduction

Interpretation : The units of cubic decimeters are to be converted into cubic millimeters.

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

Answer to Problem 52LC

The units of cubic decimeters to cubic millimeters are ${\text{10}}^6{\text{mm}}^3$ .

Explanation of Solution

Given information :

The given unit is cubic decimeters.

It is known that $\text{1}\text{dm}\text{=}{\text{10}}^2\text{mm}$ .

The dimensional analysis is a technique used for the dimensions of the measurement or units to analyze and resolve problems.

The desired conversion is ${\text{dm}}^3\to {\text{mm}}^3$ .

The conversion of the expression is given as:

  $\begin{array}{c}\text{dm}{\text{=10}}^{\text{2}}\text{mm}\left(\because \text{1}\text{dm}\text{=}{\text{10}}^{\text{2}}\text{mm}\right)\\ {\text{dm}}^{\text{3}}\text{=}{\left({\text{10}}^{\text{2}}\right)}^{\text{3}}{\text{mm}}^{\text{3}}\\ {\text{=10}}^{\text{6}}{\text{mm}}^{\text{3}}\end{array}$