Fractional part
Encyclopedia
All real number
s 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
, where 
is the floor function. It is sometimes denoted 
or 
.
If x is rational
, then the fractional part of x can be expressed in the form
, where p and q are integers and 
; hence, the fractional part will always be less than 1. For example, if 
, then the fractional part of x is .05 and can be expressed as 5/100 = 1/20.
Real number
In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...
s can be written in the form n + r where n is an integer
Integer
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...
(the integer part) and the remaining fractional part r is a nonnegative real number less than one. For a positive
Positive
Positive is a property of positivity and may refer to:- Mathematics and science :* Converging lens or positive lens, in optics* Plus sign, the sign "+" used to indicate a positive number* Positive , a polarity of electrical charge...
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
, where is the floor function. It is sometimes denoted or .If x is rational
Rational
Rational may refer to:* Rationality, a concept of reason* Rational number, a number that can be expressed as a ratio of two integers* Rational function, a mathematical function which can be written as the ratio of two polynomial functions...
, then the fractional part of x can be expressed in the form
, where p and q are integers and ; hence, the fractional part will always be less than 1. For example, if , then the fractional part of x is .05 and can be expressed as 5/100 = 1/20.See also
- Equidistributed sequence
- One-parameter groupOne-parameter groupIn mathematics, a one-parameter group or one-parameter subgroup usually means a continuous group homomorphismfrom the real line R to some other topological group G...
- Pisot–Vijayaraghavan number
- SignificandSignificandThe significand is part of a floating-point number, consisting of its significant digits. Depending on the interpretation of the exponent, the significand may represent an integer or a fraction.-Examples:...