The fractional part of a non‐negative real number
Contents
- For negative numbers
- Unique decomposition into integer and fractional parts
- Relation to continued fractions
- References
For a positive number written in a conventional positional numeral system (such as binary or decimal), its fractional part hence equals the digits appearing after the radix point.
For negative numbers
However, in case of negative numbers, there are various conflicting ways to extend the fractional part function to them: It is either defined in the same way as for positive numbers, i.e. by
with
Unique decomposition into integer and fractional parts
Under the first definition all real numbers can be written in the form
Relation to continued fractions
Every real number can be essentially uniquely represented as a continued fraction, namely as the sum of its integer part and the reciprocal of its fractional part which is written as the sum of its integer part and the reciprocal of its fractional part, and so on.