At the risk of beating the approximation topic to death.....
Here is a quick and simple exercise to show students what the basic problem is with calculators and computers.
Using pencil and paper, calculate ( 1 / 3 ) x 3.
Any student past the 5th grade should see that the threes in the numerator and denominator cancel and that the answer is exactly ONE.
Now work the same problem on any calculator: 1/3 = 0.3333333, then multiply by 3 to get (on a typical Wal-Mart variety calculator) 0.999999
Obviously, this little exercise can be extended... (1/3) x 3 x (1/5) x 5 x ( 1/7) x 7 ... etc. The point is that it is easy to get a "wrong" answer on a calculator (although the magnitude of the error will vary depending upon several things). The two questions one must always keep in mind are 1. How accurate is my answer? and 2. How accurate does it need to be?
Tom Johnson, Gilberts, IL |"I know you smoke, I know you drink that brew, I email@example.com |just can't abide a sinner like you. God can't either "Curb your dogma ... | that's why I know it to be true that Jesus loves me free your thoughts." | but he can't stand you." Austin Lounge Lizards