Chapter 5.3, Problem 1RQ

Interpretation Introduction

Interpretation: An equivalence statement needs to be explained. The number of conversion factors that can be created from one equivalent statement needs to be determined. All the possible stable conversion factors need to be written for any equivalence statement.

Concept Introduction: Equivalence is defined as a statement which relates two or more items. For examples, $2\times 3$ and $3\times 2$ have the same values thus, they are equivalent.

By a unit conversion, a same property can be expressed as a different unit of measurement. For examples, time can be expressed in minutes, hours, seconds, days, and years. One unit can be converted into other using a conversion factor.

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

Equivalent Statements are those statements whose way of expression is different, or which are written differently but there is same logical equivalence behind them.

It is possible to made two conversion factors from 1 equivalent statement.

For example, for the equivalence statement between kg to lb is as follows:

  $1\text{ kg}=2.205\text{ lb}$

Or,

  $1\text{ lb}=\frac{1}{2.205}\text{kg}=0.4535\text{ kg}$

Thus, conversion factors will be as follows:

  $\left(\frac{2.205\text{ lb}}{1\text{ kg}}\right)\text{ or }\left(\frac{\text{0}\text{.4535 kg}}{1\text{ lb}}\right)$