Exercise 1.7: The good-enough? test used
in computing square roots will not be very effective for finding the square
roots of very small numbers.  Also, in real computers, arithmetic operations
are almost always performed with limited precision.  This makes our test
inadequate for very large numbers.  Explain these statements, with examples
showing how the test fails for small and large numbers.  An alternative
strategy for implementing good-enough? is to watch how guess
changes from one iteration to the next and to stop when the change is a very
small fraction of the guess.  Design a square-root procedure that uses this
kind of end test.  Does this work better for small and large numbers?