Thanks to Brigham Young, a city block in Salt Lake City is a square one-seventh
of a mile on a side. Let's take this as the exact definition of a new unit of
measure, the ``block.''
Recall our earlier estimate that the total land area of the earth, including
inland water and Antarctica, is 57,800,000 square miles. In the problems that
follow, we will make different assumptions about its accuracy.
Use Maple to help you come up with answers to the next four questions. For
each question, give your answer along with the Maple computations that you
did in coming up with your answers.
- Assume for now that the area measure (57,800,000 square miles) is rounded
off to six significant digits. What are upper and lower bounds on the number
of blocks that make up the earth's land area?
- Now assume that the area measure can be off by plus or minus 1.25
percent. Now what are upper and lower bounds on the number of blocks that make
up the earth's land area?
- How many significant digits would be required in the square mile area
measurement for the upper and lower bounds on the number of blocks to be within
0.001 blocks of each other?
- In solving number 3, you had to use exact integer arithmetic (or else use
another feature of Maple we haven't talked about yet) to overcome a problem.
Explain what the problem was and how you got around it. Would it be possible
to solve this problem on your pocket calculator? Why or why not?
Joseph L. Zachary
Hamlet Project
Department of Computer Science
University of Utah