Chapter 5, Problem 40A

(a)

Interpretation Introduction

Interpretation: Conversion of $429$ in. to feet is needs to be explained.

Concept Introduction: To convert one unit into another then first needs to choose a conversion factor, this cancels the units and omits the units in the result. Conversion factors are the ratios of two parts of the unity report which compares two units.

Answer to Problem 40A

The conversion factor of in. to feet is $\text{35}\text{.75}\text{ft}$ .

Explanation of Solution

The equivalent statement in order to relate feet to inch is as follows:

  $1\text{ft}=12\text{in}\text{.}$

The above statement leads two conversion factor $\frac{12\text{in}\text{.}}{1\text{ft}}$ or $\frac{1\text{ft}}{12\text{in}\text{.}}$ .

Hence, for converting in. to feet second conversion factor is used.

  $\frac{1\text{ft}}{12\text{in}\text{.}}\times 429\text{in}\text{.=35}\text{.75}\text{ft}$

(b)

Interpretation Introduction

Interpretation: Conversion of converting $3.83$ ft to in. is needs to be explained.

Concept Introduction: To convert one unit into another then first needs to choose a conversion factor, this cancels the units and omits the units in the result. Conversion factors are the ratios of two parts of the unity report which compares two units.

Answer to Problem 40A

The conversion factor of $3.83\text{ft}$ to in. is $\text{45}\text{.96}\text{in}\text{.}$

Explanation of Solution

The equivalent statement in order to relate feet to inch is as follows:

  $1\text{ft}=12\text{in}\text{.}$

The above statement leads two conversion factor $\frac{12\text{in}\text{.}}{1\text{ft}}$ or $\frac{1\text{ft}}{12\text{in}\text{.}}$ .

Hence, for converting in. to feet first conversion factor is used.

  $\frac{12\text{in}\text{.}}{1\text{ft}}\times 3.83\text{ft=}\text{45}\text{.96}\text{in}\text{.}$

(c)

Interpretation Introduction

Interpretation: Conversion of converting $85.2$ mm to centimeters is needs to be explained.

Concept Introduction: To convert one unit into another then first needs to choose a conversion factor, this cancels the units and omits the units in the result. Conversion factors are the ratios of two parts of the unity report which compares two units.

Answer to Problem 40A

The conversion of $85.2$ mm to centimeters is $0.852\text{cm}$ .

Explanation of Solution

The equivalent statement in order to relate feet to inch is as follows:

  $100\text{mm}=1\text{cm}$

The above statement leads two conversion factor $\frac{100\text{mm}}{1\text{cm}}$ or $\frac{1\text{cm}}{100\text{mm}}$ .

Hence, for converting mm to centimeters second conversion factor is used.

  $\frac{1\text{cm}}{100\text{mm}}\times 85.2\text{mm}=0.852\text{cm}$

(d)

Interpretation Introduction

Interpretation: Conversion of $66.12$ cm to millimeters is needs to be explained.

Concept Introduction: To convert one unit into another then first needs to choose a conversion factor, this cancels the units and omits the units in the result. Conversion factors are the ratios of two parts of the unity report which compares two units.

Answer to Problem 40A

The conversion of $66.12$ cm to millimeters is $6612\text{mm}$ .

Explanation of Solution

The equivalent statement in order to relate feet to inch is as follows:

  $100\text{mm}=1\text{cm}$

The above statement leads two conversion factor $\frac{100\text{mm}}{1\text{cm}}$ or $\frac{1\text{cm}}{100\text{mm}}$ .

Hence, for converting mm to centimeters first conversion factor is used.

  $\frac{100\text{mm}}{1\text{cm}}\times 66.12\text{cm}=6612\text{mm}$

(e)

Interpretation Introduction

Interpretation: Conversion of $5.21$ qt to liters needs to be explained.

Concept Introduction: To convert one unit into another then first needs to choose a conversion factor, this cancels the units and omits the units in the result. Conversion factors are the ratios of two parts of the unity report which compares two units.

Answer to Problem 40A

Conversion of $5.21$ qt to liters is $4.930\text{L}$ .

Explanation of Solution

Convert $5.21\text{qt}$ into L as follows:

The conversion factor is $\frac{0.9463\text{L}}{1\text{qt}}$ to convert qt into L.

  $\begin{array}{c}1\text{quart}\left(\text{qt}\right)=0.9463\text{L}\\ \text{5}\text{.21}\text{qt}=\text{5}\text{.21}\text{qt}\times \frac{0.9463\text{L}}{1\text{qt}}\\ =4.930\text{L}\end{array}$

(f)

Interpretation Introduction

Interpretation: Convert $14.8$ pt to quarts needs to be explained.

Concept Introduction: To convert one unit into another then first needs to choose a conversion factor, this cancels the units and omits the units in the result. Conversion factors are the ratios of two parts of the unity report which compares two units.

Answer to Problem 40A

Conversion of $14.8$ pt to quarts is $8.89\text{quart}$ .

Explanation of Solution

The equivalent statement in order to relate pt to quart is as follows:

  $1\text{pt}=0.600475\text{quart}$

The above statement leads two conversion factor $\frac{0.600475\text{quart}}{1\text{pt}}$ or $\frac{1\text{pt}}{0.600475\text{quart}}$ .

Convert $14.8$ pt to quarts as follows:

Hence, for converting pt to quart first conversion factor is used.

  $\frac{0.600475\text{quart}}{1\text{pt}}\times 14.8\text{pt}=8.89\text{quart}$

(g)

Interpretation Introduction

Interpretation: Conversion factor of converting $22.4$ lb to kilograms is needs to be explained.

Concept Introduction: To convert one unit into another then first needs to choose a conversion factor, this cancels the units and omits the units in the result. Conversion factors are the ratios of two parts of the unity report which compares two units.

Answer to Problem 40A

Conversion of $22.4$ lb to kilograms is $10.16\text{kg}$ .

Explanation of Solution

Convert $22.4$ lb into kg as follows:

  $1\text{lb}=0.4535\text{kg}$

The above statement leads two conversion factor $\frac{1\text{lb}}{0.4535\text{kg}}$ or $\frac{0.4535\text{kg}}{1\text{lb}}$ .

Convert lb into kg as follows:

  $\begin{array}{c}1\text{lb}=0.4535\text{kg}\\ 22.4\text{lb}=22.4\text{lb}\times \frac{0.4535\text{kg}}{1\text{lb}}\\ =10.16\text{kg}\end{array}$

(h)

Interpretation Introduction

Interpretation: Conversion factor of converting $18.6$ oz to pounds is needs to be explained.

Concept Introduction: To convert one unit into another then first needs to choose a conversion factor, this cancels the units and omits the units in the result. Conversion factors are the ratios of two parts of the unity report which compares two units.

Answer to Problem 40A

Conversion of $18.6$ oz to pounds is $1.625\text{pound}$ .

Explanation of Solution

Convert $18.6$ oz to pounds follows:

  $1\text{oz}=0.0625\text{pound}$

The above statement leads two conversion factor $\frac{1\text{oz}}{0.0625\text{pound}}$ or $\frac{0.0625\text{pound}}{1\text{oz}}$ .

Convert oz into pounds as follows:

  $\frac{0.0625\text{pound}}{1\text{oz}}\times 18.6\text{oz}=1.625\text{pound}$