Chapter 6.6, Problem 15P

* Suppose you need to know how many thirty-secondths $\left(\frac{1}{32}\right)$ of an inch 0.685 inch is (rounded to the nearest thirty-secondth of an inch). Explain why the following method is a legitimate way to solve this problem:
• Calculate $0.685\times 21.92,$and round the result to the nearest whole number, namely, 22.
• Use your result from the previous step, 22, to form the fraction $\frac{22}{32}.$ Then 0.685 inch is $\frac{22}{32}$ inch rounded to the nearest thirty-secondth of an inch.
Don't just verify that this method gives the right answer; explain why it works.