posted on Mar, 24 2005 @ 07:16 AM
.333 x 3= .999
You can't do the inverse of the operation due to round off error
. When the original calculation was made ( 1 ÷ 3), the decision was made to
drop off part of the value. The all powerful computer (No matter which one you choose) does not have enough memory to represent the digit 3 carrying
on to infinity. This brings up a lot of issues such as the black hole forming near the infinite amount of mass used to store the infinite amount of
memory. That and the fact that most wimpy manufacturers only give you 3-4 banks to put memory cards in, ect.
So for lack of memory, we make the decision to only keep the first million digits or so. And this is all fine since the result is close enough to give
out the correct change or to put a shuttle in space. Now when you try to use the result in a calculation, you just blew it. You're now compounding
the problem since you're starting with a flawed number to begin with.
Say you need a 6 foot ladder to reach a light bulb, and you have one that's 5 1/2 feet tall. Close enough right? Sure, you can still reach the light
bulb with no problem. But now if you try to add two of your almost 6 feet
ladders to make a 12 ft. ladder you're off by a whole foot. If you
tried to combine your incomplete ladders to reach the top of a 20 story building, you would be way, way, way, way, off. How much round off we allow
depends on how important the calculation is. For a one time calculation, we don't care that much, but........
An egregious example of roundoff error is provided by a short-lived index devised at the Vancouver stock exchange (McCullough and Vinod 1999).
At its inception in 1982, the index was given a value of 1000.000. After 22 months of recomputing the index and truncating to three decimal places at
each change in market value, the index stood at 524.881, despite the fact that its "true" value should have been 1009.811.
In short, you've just stepped out of the protective world of integers, and ran into "real world math" or real numbers. It can be a bit scary at
times. Also, try not to reuse numbers that have been rounded.