Chapter 5.3, Problem 3RQ

(a)

Interpretation Introduction

Interpretation: The conversion from inch to centimetre needs to be performed.

Concept Introduction: A conversion factor is defined as number which is used to change one unit to other by either multiplying or dividing. For example, in 1 minute there are 60 seconds and 1 second corresponds to 0.0167 minutes. Thus, for conversion between minutes and seconds, conversion factors used will be $\frac{60\text{ seconds}}{1\text{ minute}}$ or $\frac{0.0167\text{ minutes}}{1\text{ second}}$

Explanation of Solution

Both the given units are for length. Here, in. expresses inch and cm expresses centimetre. The given statement is an equivalence statement thus, there are two possible conversion factors for it. One conversion factor shows conversion of in. to cm and other shows cm to in.

Since,

  $1\text{ in}\text{.}=\text{2}\text{.54 cm}$

Or,

  $1\text{ cm}=\frac{1}{\text{2}\text{.54}}\text{ in}\text{.}=\text{0}\text{.394 in}\text{.}$

Thus, conversion factors will be as follows:

  $\left(\frac{\text{0}\text{.394 in}.}{\text{1 cm}}\right)\text{ or }\left(\frac{\text{2}\text{.54 cm}}{1\text{ in}\text{.}}\right)$

Now, given conversion can be performed as follows:

  $14\text{ in}\text{.}\left(\frac{2.54\text{ cm}}{1\text{ in}\text{.}}\right)=35.56\text{ cm}$

(b)

Interpretation Introduction

Interpretation: The conversion from g to lb needs to be performed.

Concept Introduction: A conversion factor is defined as number which is used to change one unit to other by either multiplying or dividing. For example, in 1 minute there are 60 seconds and 1 second corresponds to 0.0167 minutes. Thus, for conversion between minutes and seconds, conversion factors used will be $\frac{60\text{ seconds}}{1\text{ minute}}$ or $\frac{0.0167\text{ minutes}}{1\text{ second}}$

Explanation of Solution

Both the given units are for mass. Here, g expresses grams and lb express pounds. The given statement is an equivalence statement thus, there are two possible conversion factors for it. One conversion factor shows conversion of g to lb and other shows from lb to g.

Since,

  $1\text{ g}=0.0022\text{ lb}$

Or,

  $1\text{ lb}=\frac{1}{0.0022}\text{g}=454.5\text{ g}$

Thus, conversion factors will be as follows:

  $\left(\frac{0.0022\text{lb}}{1\text{ g}}\right)\text{ or }\left(\frac{\text{454}\text{.5 g}}{1\text{ lb}}\right)$

Now, given conversion can be performed as follows:

  $2138\text{ g}\left(\frac{0.0022\text{lb}}{1\text{ g}}\right)=4.70\text{ lb}$

(c)

Interpretation Introduction

Interpretation: The conversion from L to qt needs to be performed.

Concept Introduction: A conversion factor is defined as number which is used to change one unit to other by either multiplying or dividing. For example, in 1 minute there are 60 seconds and 1 second corresponds to 0.0167 minutes. Thus, for conversion between minutes and seconds, conversion factors used will be $\frac{60\text{ seconds}}{1\text{ minute}}$ or $\frac{0.0167\text{ minutes}}{1\text{ second}}$

Explanation of Solution

Both the given units are for volume Here, L expresses litre and qt express US liquid quarts. The given statement is an equivalence statement thus, there are two possible conversion factors for it. One conversion factor shows conversion of L to qt and other shows from qt to L.

Since,

  $1\text{ L}=1.056\text{ qt}$

Or,

  $1\text{ qt}=\frac{1}{1.056}\text{ L}=0.947\text{ L}$

Thus, conversion factors will be as follows:

  $\left(\frac{1.056\text{ qt}}{1\text{ L}}\right)\text{ or }\left(\frac{\text{0}\text{.947 L}}{1\text{ qt}}\right)$

Now, the given conversion can be performed as follows:

  $18.2\text{ L}\left(\frac{1.056\text{ qt}}{1\text{ L}}\right)=19.22\text{ qt}$

(d)

Interpretation Introduction

Interpretation: The conversion from yd to mi needs to be performed.

Concept Introduction: A conversion factor is defined as number which is used to change one unit to other by either multiplying or dividing. For example, in 1 minute there are 60 seconds and 1 second corresponds to 0.0167 minutes. Thus, for conversion between minutes and seconds, conversion factors used will be $\frac{60\text{ seconds}}{1\text{ minute}}$ or $\frac{0.0167\text{ minutes}}{1\text{ second}}$

Explanation of Solution

Both the given units are for distance. Here, yd expresses yard and mi express miles The given statement is an equivalence statement thus, there are two possible conversion factors for it. One conversion factor shows conversion of yd to mi and other shows from mi to yd.

Since,

  $1\text{ yd}=0.000568\text{ mi}$

Or,

  $1\text{ mi}=\frac{1}{0.000568}\text{yd}=1760\text{ yd}$

Thus, conversion factors will be as follows:

  $\left(\frac{0.000568\text{ mi}}{1\text{ yd}}\right)\text{ or }\left(\frac{\text{1760 yd}}{1\text{ mi}}\right)$

Now, given conversion can be performed as follows:

  $14500\text{ yd}\left(\frac{0.000568\text{ mi}}{1\text{ yd}}\right)=8.236\text{ mi}$