Our implementation now looks pretty solid, so let's take a critical look at the
method that we used to arrive at it. Recall that we chose to calculate the
area of a sphere using the classical formula. What approximation did that
introduce?
Click here for the answer
There is no way to eliminate this approximation entirely, since any finite
value that we use for will be inexact. We have no choice but to be
honest about the limitations of our computation. What is ``dishonest'' about
using 1,018,260.48 square feet as our answer?
Click here for the answer
When doing a multiplication or a division, there will never be more
significant digits in the final answer than there were in the least
precise input value. In fact, there may even be fewer significant digits than
that. For example, suppose that you multiply two numbers, where one has seven
significant digits and the other has two. The product will contain zero, one,
or two significant digits, but no more.
If we assume that 3.14 is an accurate value of to three significant
digits, and that the other numbers that we used in our computation were exact,
only the first three digits in our final answer can possibly be significant.
We are thus obliged to round our answer off to three digits to obtain 1,020,000
square feet. We must also report that no more than the first three digits, and
possibly fewer, are significant. We will shortly see how to more accurately
determine which of the digits in an answer are actually significant.
Joseph L. Zachary
Hamlet Project
Department of Computer Science
University of Utah