Chapter 3, Problem 19E

Interpretation Introduction

(a)

Interpretation:

The equivalency and both conversion factor a) minutes and seconds is to be stated.

Concept introduction:

Equivalency is defined as the two quantities that are equivalent in value. For example: 0.025 furlong is equal to 1 rod. In this case, furlong and rod represent the same physical length but expressed in various units. When an equivalency is denoted as a fractional value it is called ‘conversion factor’. Moreover, two conversion factors result from each equivalency.

Answer to Problem 19E

The equivalency of a) minutes and seconds is $1\mathrm{ }\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{u}\mathrm{t}\mathrm{e}\mathrm{ }=\mathrm{ }60\mathrm{ }\mathrm{s}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}\mathrm{s}$

Conversion factors of a) minutes and seconds are given by;

$\frac{\text{1minute}}{\text{60seconds}}\text{and}\frac{\text{60}\text{seconds}}{\text{1minute}}$

Explanation of Solution

The two quantities that are equivalent in value is denoted as equivalence. For example: $0.025$ furlong is equal to 1 rod. In this case, furlong and rod represent the same physical length but expressed in various units. When an equivalency is denoted as a fractional value it is called ‘conversion factor’. Moreover, two conversion factors result from each equivalency.

$\begin{array}{l}\text{0}\text{.025}\text{furlong = 1}\text{rog}\\ \frac{\text{0}\text{.025}\text{furlong}}{\text{1}\text{rod}}\text{(and)}\frac{\text{1}\text{rod}}{\text{0}\text{.025}\text{furlong}}\cdot \cdot \cdot (1)\end{array}$

In the expression (1), the conversion factor $\frac{\text{1}\text{rod}}{\text{0}\text{.025}\text{furlong}}$ is used to convert a length expressed in furlongs to a length expressed in rods. Two variable, x and y are directly proportional if there is a non-zero constant k which connect them in the form of $y = kx$. Besides, the relationship is expressed as $y \alpha x$. In the expression the symbol α is called as ‘is proportional to’.

A proportionality constant, m is inserted to convert a proportionality into an equality. Such as,

$y=m\cdot x\cdot \cdot \cdot (2)$

Given expression;

a) Minutes and seconds

Based on the above discussion the equivalency and conversion factors are states as follows;

The equivalency of a) minutes and seconds is $1\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{u}\mathrm{t}\mathrm{e}\mathrm{ }=\mathrm{ }60\mathrm{ }\mathrm{s}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}\mathrm{s}$

Conversion factors of a) minutes and seconds are given by;

$\frac{\text{1minute}}{\text{60seconds}}\text{and}\frac{\text{60}\text{seconds}}{\text{1minute}}$

Conclusion

Thus, the equivalency and both conversion factor a) minutes and seconds is to be stated

Interpretation Introduction

(b)

Interpretation:

The equivalency and both conversion factor b) inches and feet is to be stated

Concept introduction:

Equivalency is defined as the two quantities that are equivalent in value. For example: $0.025$$\mathrm{f}\mathrm{u}\mathrm{r}\mathrm{l}\mathrm{o}\mathrm{n}\mathrm{g}$ is equal to $1\mathrm{ }\mathrm{r}\mathrm{o}\mathrm{d}$. In this case, furlong and rod represent the same physical length but expressed in various units. When an equivalency is denoted as a fractional value it is called ‘conversion factor’. Moreover, two conversion factors result from each equivalency.

Answer to Problem 19E

The equivalency of b) inches and feet is $12\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{c}\mathrm{h}\mathrm{e}\mathrm{s}\mathrm{ }=\mathrm{ }1\mathrm{ }\mathrm{f}\mathrm{o}\mathrm{o}\mathrm{t}$

Conversion factors of b) inches and feet are given by;

$\frac{\text{12}\text{inches}}{\text{1}\text{foot}}\text{and}\frac{\text{1foot}}{\text{12inches}}$

Explanation of Solution

The two quantities that are equivalent in value is denoted as equivalence. For example: 0.025 furlong is equal to 1 rod. In this case, furlong and rod represent the same physical length but expressed in various units. When an equivalency is denoted as a fractional value it is called ‘conversion factor’. Moreover, two conversion factors result from each equivalency.

$\begin{array}{l}\text{0}\text{.025}\text{furlong = 1}\text{rog}\\ \frac{\text{0}\text{.025}\text{furlong}}{\text{1}\text{rod}}\text{(and)}\frac{\text{1}\text{rod}}{\text{0}\text{.025}\text{furlong}}\cdot \cdot \cdot (1)\end{array}$

In the expression (1), the conversion factor $\frac{\text{1}\text{rod}}{\text{0}\text{.025}\text{furlong}}$ furlong is used to convert a length expressed in furlongs to a length expressed in rods. Two variable, x and y are directly proportional if there is a non-zero constant k which connect them in the form of y = kx. Besides, the relationship is expressed as $y \alpha x$. In the expression the symbol α is called as ‘is proportional to’.

A proportionality constant, m is inserted to convert a proportionality into an equality. Such as,

$y=m\cdot x\cdot \cdot \cdot (2)$

Given expression;

b) Inches and feet

Based on the above discussion the equivalency and conversion factors are states as follows;

The equivalency of inches and feet is $12\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{c}\mathrm{h}\mathrm{e}\mathrm{s}\mathrm{ }=\mathrm{ }1\mathrm{ }\mathrm{f}\mathrm{o}\mathrm{o}\mathrm{t}$

Conversion factors of inches and feet are given by;

$\begin{array}{l}\frac{\text{1}\text{dolloar}}{\text{100}\text{cents}}\text{and}\frac{\text{100}\text{cents}}{\text{1}\text{dolloar}}\\ \end{array}$

Conclusion

Thus, the equivalency and both conversion factor inches and feet is to be stated

Interpretation Introduction

(c)

Interpretation:

The equivalency and both conversion factor c) dollars and cents is to be stated

Concept introduction:

Equivalency is defined as the two quantities that are equivalent in value. For example: $0.025\mathrm{ }\mathrm{f}\mathrm{u}\mathrm{r}\mathrm{l}\mathrm{o}\mathrm{n}\mathrm{g}$ is equal to 1 rod. In this case, furlong and rod represent the same physical length but expressed in various units. When an equivalency is denoted as a fractional value it is called ‘conversion factor’. Moreover, two conversion factors result from each equivalency.

Answer to Problem 19E

The equivalency of c) dollars and cents is 1 dollar = 100 cents

Conversion factors of c) dollars and cents are given by;

$\frac{\text{1}\text{dolloar}}{\text{100}\text{cents}}\text{and}\frac{\text{100}\text{cents}}{\text{1}\text{dolloar}}$

Explanation of Solution

The two quantities that are equivalent in value is denoted as equivalence. For example: $0.025\mathrm{ }\mathrm{f}\mathrm{u}\mathrm{r}\mathrm{l}\mathrm{o}\mathrm{n}\mathrm{g}$ is equal to $1\mathrm{ }\mathrm{r}\mathrm{o}\mathrm{d}$. In this case, furlong and rod represent the same physical length but expressed in various units. When an equivalency is denoted as a fractional value it is called ‘conversion factor’. Moreover, two conversion factors result from each equivalency.

$\begin{array}{l}\text{0}\text{.025}\text{furlong = 1}\text{rog}\\ \frac{\text{0}\text{.025}\text{furlong}}{\text{1}\text{rod}}\text{(and)}\frac{\text{1}\text{rod}}{\text{0}\text{.025}\text{furlong}}\cdot \cdot \cdot (1)\end{array}$

In the expression (1), the conversion factor $\frac{\text{1}\text{rod}}{\text{0}\text{.025}\text{furlong}}\text{furlong}$ is used to convert a length expressed in furlongs to a length expressed in rods. Two variable, x and y are directly proportional if there is a non-zero constant k which connect them in the form of y = kx. Besides, the relationship is expressed as y α x. In the expression the symbol α is called as ‘is proportional to’.

A proportionality constant, m is inserted to convert a proportionality into an equality. Such as,

$y=m\cdot x\cdot \cdot \cdot (2)$

Given expression;

c) dollars and cents

Based on the above discussion the equivalency and conversion factors are states as follows;

The equivalency of c) dollars and cents is 1 dollar = 100 cents

Conversion factors of c) dollars and cents are given by;

$\frac{\text{1}\text{dolloar}}{\text{100}\text{cents}}\text{and}\frac{\text{100}\text{cents}}{\text{1}\text{dolloar}}$

Conclusion

Thus, the equivalency and both conversion factor dollars and cents is to be stated