Chapter 3.3, Problem 41SP

Interpretation Introduction

Interpretation : The expression of $0.044\text{km}$ to meters 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 41SP

The expression of $0.044\text{km}$ is $44\text{ m}$ .

Explanation of Solution

Given information :

The given expression is $0.044\text{km}$ .

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

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

The conversion of the expression is given as

  $\begin{array}{c}0.044\text{km =}0.044\cancel{\text{km}}\times \frac{{10}^3\text{m}}{1\cancel{\text{km}}}\left(\because \text{1}\text{km}\text{=}{\text{10}}^3\text{m}\right)\\ =44\text{ m}\end{array}$

Interpretation Introduction

Interpretation : The expression of $4.6\text{mg}$ to grams 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 41SP

The expression of $4.6\text{mg}$ is $4.6\times {10}^{-3}\text{g}$ .

Explanation of Solution

Given information :

The given expression is $4.6\text{mg}$ .

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

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

The conversion of the expression is given as

  $\begin{array}{c}4.6\text{mg}\text{=}4.6\cancel{\text{mg}}\times \frac{{10}^{-3}\text{g}}{1\cancel{\text{mg}}}\left(\because \text{1}\text{g}\text{=}{\text{10}}^3\text{mg}\right)\\ =4.6\times {10}^{-3}\text{g}\end{array}$

Interpretation Introduction

Interpretation : The expression of $0.107\text{g}$ to centigrams 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 41SP

The expression of $0.107\text{g}$ is $\text{1}{\text{.07×10}}^1\text{cg}$ .

Explanation of Solution

Given information :

The given expression is $0.107\text{g}$ .

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

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

The conversion of the expression is given as

  $\begin{array}{c}0.107\text{g}\text{=}0.107\cancel{\text{g}}\times \frac{{10}^2\text{cg}}{1\cancel{\text{g}}}\left(\because \text{1}\text{g}\text{=}{\text{10}}^2\text{cg}\right)\\ =1.07\times {10}^1\text{cg}\end{array}$