Here are three facts about significant digits, the first of which you learned
in the last lesson. Don't simply memorize these facts--be sure that they make
sense to you.
- The number of significant digits in a product or quotient is no greater
than the number of significant digits in the least precise of the operands.
For example, if we multiply a number with three significant digits by a number
with two significant digits, the answer will contain two or fewer significant
digits.
- The number of significant digits in a sum or difference is no greater
than the number of significant digits in the numerically larger of the
operands. For example, if we add a large number with three significant digits
to a small number with two significant digits, the answer will contain three or
fewer significant digits.
- The number of significant digits in an answer can never be greater than
the number of significant digits in every operand. For example, if we take the
square root of a number with two significant digits, the answer will contain
two or fewer significant digits.
The answer that we obtained in the last section was 39,854.7 feet. Based upon
the facts above and your intuition, at most how many of those digits may be
significant?
Click here for the answer
Thus, the best way to phrase our answer is to say that from the top of Kitty
Hawk, one can see 40,000 feet out into Albemarle Sound, where at most two of
the digits in the answer are significant.
Joseph L. Zachary
Hamlet Project
Department of Computer Science
University of Utah