= Floating-point number
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, $1/2$ is exact but $1/10$ 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.<IEEE arithmetic in Oracle's Numerical Computation Guide>[§2.2, IEEE formats]{ref}
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