Fractional part

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All real numbers can be written in the form n + r where n is an integer (the integer part) and the remaining fractional part r is a nonnegative real number less than one. For a positive number written in decimal notation, the fractional part corresponds to the digits appearing after the decimal point.

The fractional part of a real number x is x-\lfloor x\rfloor, where \lfloor\;\rfloor is the floor function. It is sometimes denoted \{x\}, \langle x \rangle or x\,\bmod\,1.

If x is rational, then the fractional part of x can be expressed in the form p / q, where p and q are integers and  0 \le p < q . For example, if  x = 1.05 , then the fractional part of x is .05 and can be expressed as 5/100 = 1/20.

The fractional part of negative numbers does not have a universal definition. It is either defined as x-\lfloor x\rfloor (Graham, Knuth & Patashnik 1992) or as the part of the number to the right of the radix point (Daintith 2004). For example, the number -1.3 has a fractional part of 0.7 according to the first definition and 0.3 according to the second definition.

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