 Dyadic rational

A dyadic rational is a rational number of the form $m/2^k$ with an integer $m$ and a nonnegative integer $k$. Examples are $3/8$, $-5/2$, zero and every integer. In lowest terms, its denominator is a power of two, so its magnitude has a finite binary expansion.

A positive dyadic rational also has a binary representation ending in infinitely many ones. Replacing the last nonzero binary digit by zero and filling all lower places with ones preserves the value, becauseFor example, $0.101_2=0.100111{\dots }_2=5/8$. Zero has no second nonnegative expansion of this type. The same ambiguity applies to the magnitude of a negative dyadic rational, with its sign kept separately.

A dyadic rational is a type of number in the form of \(\frac{m}{2^n}\), where \(m\) is an integer and \(n\) is a non-negative integer. In other words, dyadic rationals are fractions where the denominator is a power of 2.