Chapter 2, Problem 102A

Interpretation Introduction

Interpretation:

The given conversion needs to be evaluated..

$\text{rate}=\frac{\text{75}\text{m}}{\text{1}\text{s}}\times \frac{\text{60}\text{s}}{\text{1}\text{min}}\times \frac{\text{1}\text{h}}{\text{60}\text{min}}$

Concept introduction:

Unit conversion can be defined as a multi-step process involving division or multiplication by a numerical factor, rounding and selection of correct number of significant digits.

Answer to Problem 102A

The given conversion is not true as it fails to cancel out the units correctly.

Explanation of Solution

Rate should be distance (given in any units i.e. meters, centimeters, feet kilometers etc.) divided by time (seconds, minutes hours etc.).

$\begin{array}{c}\text{rate}=\frac{\text{75}\text{m}}{\text{1}\text{s}}\times \frac{\text{60}\text{s}}{\text{1}\text{min}}\times \frac{\text{1}\text{h}}{\text{60}\text{min}}\\ =\frac{75\text{mh}}{60{\min }^2}\\ =1.25{\text{mh/min}}^{\text{2}}\end{array}$

The given conversion is not true as it fails to cancel out the units correctly. In the give conversion, the number of minutes is not correctly set up. The number of minutes in 1 hour needs to be turn over which mean the hours must be in denominator to give the correct conversion i.e. m/s.

Conclusion

The given conversion is not true as it fails to cancel out the units correctly.