Chapter 5, Problem 43A

Interpretation Introduction

Interpretation: The train that reaches the speed of 225mi/h to be calculated.

Concept introduction: Scientific notation is quantitative information is called a measurement and exists of a number and a unit. By using scientific notation too large or too small numbers are conveniently expressed.

Answer to Problem 43A

Train going from Boston to New York is faster than those in United Kingdom.

Explanation of Solution

Relationship between mile and kilometers is as follows:

Given 1mile = 1.6093kilometers

Conversion factor of this statement is as follows:

  $\frac{\text{1mi}}{\text{1}\text{.6093kilometers}}\text{or}\frac{\text{1}\text{.6093kilometers}}{\text{1}\text{mi}}$

The speeds must share the same units to determine whether the train running from Boston to New York is faster than trains. Following dimensional analysis can be done ro convert the speed of the train from Boston and New York.

  $\frac{\text{160mi}}{\text{h}}\text{×}\frac{\text{1}\text{.6093kilometers}}{\text{1mi}}\text{=257}\text{.488}\text{kilometers}/\text{h}$

Conversion of 225km/h to mi/h is as follows:

  $\begin{array}{c}\frac{\text{225}\cancel{\text{km}}}{\text{h}}\text{×}\frac{\text{1mi}}{\text{1}\text{.6093}\cancel{\text{km}}}\text{=139}\text{.81}\text{mi}/\text{h}\\ =1.40\times {10}^2\text{mi}/\text{h}\end{array}$

225 has three significant digits. Thus to give correct numbers of significant digits the answer is written as $1.40\times {10}^2\text{mi}/\text{h}$ .

Train going from Boston to New York is faster than those in United Kingdom.

Conclusion

Inherent uncertainty of measuring device determines number of significant figures for a given measurement.