Zach Rode wrote:Tim, does the 1/2 point of precision effectively become useless in calculations?
It's not so much "useless" as it is a warning. Floating-point numbers are fuzzy. Let me return to my decimal example.
If you divide 1 by 3, you get 0.333333333.....
Technically, this is "useless", because it will never
precisely represent 1/3 this side of infinity.
The same applies to 1/10 in binary. 1/2 or 1/4 can be represented precisely in binary, but 1/10 cannot. However, just as "1.333" can be "close enough for Government work"*, the binary equivalent of 1/10 is likewise. It isn't exact, which is why bookkeeping systems should never use floating point (this is where the infamous "penny-shaving" fraud comes from), but it's perfectly fine for higher-level computations like sales projections.
If memory serves, the potential error has the technical name "epsilon". For best accuracy, the epsilon value should be as small as possible relative to the accuracy actually needed. For example, if your numbers are only accurate to 3-1/2 places, then trying to work with 4 digits is going be more perception than precision. Ultimately, the whole thing falls into the basic Calculus concepts of Range and Domain and computing how precise a value is going to be after all the necessary computing is done.
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* Literally, in some cases.