A finite floating-point number is a value representable in a specified floating-point representation. For fixed precision and exponent bounds, only finitely many real values are available. Most real numbers therefore require rounding before storage.
In binary arithmetic, is exact but is not: a finite binary fraction has a reduced denominator that is a power of two. This is a property of the representation, even before any arithmetic operation occurs. The associated IEEE encodings additionally include infinities and NaN; NaN is a special arithmetic datum rather than a real value.[ref]
