Chapter 3, Problem 77A

a)

Interpretation Introduction

Interpretation : The units in milligrams 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 77A

The unit in milligrams is $2.83\times {10}^2\text{mg}$ .

Explanation of Solution

Given information :

The given value is $28.3\text{cg}$ .

It is known that $\text{1}\text{cg}\text{=}\text{10}\text{mg}$ .

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

The conversion of the units is given as

  $\begin{array}{c}28.3\text{cg}=28.3\text{cg}\times \frac{10\text{mg}}{1\text{cg}}\left(\because \text{1}\text{cg}\text{=}\text{10}\text{mg}\right)\\ =283\text{mg}\\ \text{=}\text{2}\text{.83}\times {\text{10}}^2\text{mg}\end{array}$

b)

Interpretation Introduction

Interpretation : The units in grams 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 77A

The unit in gram is $0.283\text{g}$ .

Explanation of Solution

Given information :

The given value is $28.3\text{cg}$ .

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

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

The conversion of the units is given as

  $\begin{array}{c}28.3\text{cg}=28.3\cancel{\text{cg}}\times \frac{{10}^{-2}\text{g}}{1\cancel{\text{cg}}}\left(\because \text{1}\text{g}\text{=}{\text{10}}^2\text{cg}\right)\\ =0.283\text{g}\end{array}$

c)

Interpretation Introduction

Interpretation : The unit in kilogram 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 77A

The unit in kilogram is $2.83\times {10}^{-4}\text{kg}$ .

Explanation of Solution

Given information :

The given value is $28.3\text{cg}$ .

It is known that $1\text{kg}\text{=}{\text{10}}^5\text{cg}$ .

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

The conversion of the units is given as

  $\begin{array}{c}28.3\text{cg}=28.3\cancel{\text{cg}}\times \frac{{10}^{-5}\text{kg}}{1\cancel{\text{cg}}}\left(\because 1\text{kg}\text{=}{\text{10}}^5\text{cg}\right)\\ =2.83\times {10}^{-4}\text{kg}\end{array}$

d)

Interpretation Introduction

Interpretation : The units in grams 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 77A

The unit in gram is $6.6\text{g}$ .

Explanation of Solution

Given information :

The given value is $6.6\times {10}^3\text{mg}$ .

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

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

The conversion of the units is given as

  $\begin{array}{c}6.6\times {10}^3\text{mg}=6.6\times \cancel{{10}^3}\cancel{\text{mg}}\times \frac{\cancel{{10}^{-3}}\text{g}}{1\cancel{\text{mg}}}\left(\because \text{1}\text{g}\text{=}{10}^3\text{mg}\right)\\ =6.6\text{g}\end{array}$

e)

Interpretation Introduction

Interpretation : The units in centigrams 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 77A

The unit in centigram is $6.6\times {10}^2\text{cg}$ .

Explanation of Solution

Given information :

The given value is $6.6\times {10}^3\text{mg}$ .

It is known that $\text{1}\text{mg}\text{=}{\text{10}}^{-1}\text{cg}$ .

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

The conversion of the units is given as

  $\begin{array}{c}6.6\times {10}^3\text{mg}=6.6\times {10}^3\cancel{\text{mg}}\times \frac{{10}^{-1}\text{cg}}{1\cancel{\text{mg}}}\left(\because \text{1}\text{mg}\text{=}{\text{10}}^{-1}\text{cg}\right)\\ =6.6\times {10}^2\text{cg}\end{array}$

f)

Interpretation Introduction

Interpretation : The unit in kilogram 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 77A

The unit in kilogram is $6.6\times {10}^{-3}\text{kg}$ .

Explanation of Solution

Given information :

The given value is $6.6\times {10}^3\text{mg}$ .

It is known that $1\text{kg}\text{=}{\text{10}}^6\text{mg}$ .

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

The conversion of the units is given as

  $\begin{array}{c}6.6\times {10}^3\text{mg}=6.6\times {10}^3\cancel{\text{mg}}\times \frac{{10}^{-6}\text{kg}}{1\cancel{\text{mg}}}\left(\because 1\text{kg}\text{=}{\text{10}}^6\text{mg}\right)\\ =6.6\times {10}^{-3}\text{kg}\end{array}$

g)

Interpretation Introduction

Interpretation : The units in milligrams 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 77A

The unit in milligram is $2.8\times {10}^{-1}\text{mg}$ .

Explanation of Solution

Given information :

The given value is $2.8\times {10}^{-4}\text{g}$ .

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

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

The conversion of the units is given as

  $\begin{array}{c}2.8\times {10}^{-4}\text{g}=2.8\times {10}^{-4}\cancel{\text{g}}\times \frac{{10}^3\text{mg}}{1\cancel{\text{g}}}\left(\because 1\text{g}\text{=}{\text{10}}^3\text{mg}\right)\\ =2.8\times {10}^{-1}\text{mg}\end{array}$

h)

Interpretation Introduction

Interpretation : The units in centigrams 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 77A

The unit in centigram is $2.8\times {10}^{-2}\text{cg}$ .

Explanation of Solution

Given information :

The given value is $2.8\times {10}^{-4}\text{g}$ .

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 units is given as

  $\begin{array}{c}2.8\times {10}^{-4}\text{g}=2.8\times {10}^{-4}\cancel{\text{g}}\times \frac{{10}^2\text{cg}}{1\cancel{\text{g}}}\left(\because \text{1}\text{g}\text{=}{\text{10}}^2\text{cg}\right)\\ =2.8\times {10}^{-2}\text{cg}\end{array}$

i)

Interpretation Introduction

Interpretation : The unit in kilogram 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 77A

The unit in kilogram is $2.8\times {10}^{-7}\text{kg}$ .

Explanation of Solution

Given information :

The given value is $2.8\times {10}^{-4}\text{g}$ .

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

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

The conversion of the units is given as

  $\begin{array}{c}2.8\times {10}^{-4}\text{g}=2.8\times {10}^{-4}\cancel{\text{g}}\times \frac{{10}^{-3}\text{kg}}{1\cancel{\text{g}}}\left(\because \text{1}\text{kg}\text{=}{10}^3\text{g}\right)\\ =2.8\times {10}^{-7}\text{kg}\end{array}$