Chapter 5, Problem 36A

Interpretation Introduction

Interpretation: The conversion factor that is appropriate to convert 1849 yd to miles and 2.781 mi to yards 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 36A

  $\text{1849yd=1}\text{.05056818mi}$

  $\text{2}\text{.781mi=4894}\text{.56yd}$

Explanation of Solution

Significant figures are first uncertain number plus all certain numbers.

Given 1mi = 1760 yd.

Conversion factor of this statement is as follows:

  $\frac{\text{1mi}}{\text{1760yd}}\text{or}\frac{\text{1760}\text{yd}}{\text{1}\text{mi}}$

Conversion of 1849 to miles is as follows:

  $\text{1849}\cancel{\text{yd}}\text{×}\frac{\text{1mi}}{\text{1}\text{760}\cancel{\text{yd}}}\text{=1}\text{.05056818mi}$

Conversion of 2.781 mi to yard is as follows:

  $\text{2}\text{.781}\cancel{\text{mi}}\text{×}\frac{\text{1760yd}}{\text{1}\cancel{\text{mi}}}\text{=4894}\text{.56yd}$

Conclusion

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