The conventional system of number representation cannot exactly represent most numbers. Fractions that have factors in the denominator that are not in the number system's base have infinite decimal representations (e.g. other than 2 and 5 for base 10). Square roots and other irrational numbers \ have infinite, non-repeating representations.
In the late 1990s I came up with an alternative system that can exactly represent any rational or irrational number as well as most transcendental numbers using only a finite number of bits. This type of representation is based upon the idea of factored representations of integers extended in a logical way to a nearly universal system of describing number structure.
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