Jonathan M Davis wrote:
It may be that you would still end up with situations where two values that you would think would be the same aren't due to rounding error or whatnot. However, with a fixed point value, you wouldn't have the problem where a particular value could not be held in it even if it's within its range of precision. As I understand it, there are a number of values which cannot be held in a floating point and therefore end up being rounded up or down simply because of how floating points work and not because there the precision isn't high enough.
That happens with decimal representations, too, just with a different set of numbers.
It's definitely true however, that using fractions would be much more accurate for a lot of stuff. That wouldn't be particulary efficient though. Still, if you're doing a lot of math that needs to be accurate, that may be the way to go.
The set of irrational numbers cannot (by definition) be represented by a ratio. For example, the square root of 2.
