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In mathematics, "rational" is often used as a noun abbreviating "rational number". The adjective rational sometimes means that the coefficients are rational numbers. For example, a rational point is a point with rational coordinates (i.e., a point whose coordinates are rational numbers); a rational matrix is a matrix of rational numbers; a rational polynomial may be a polynomial with rational ...
Pages in category "Rational numbers" The following 12 pages are in this category, out of 12 total. ... Contact Wikipedia; Code of Conduct; Developers; Statistics;
Some programming languages provide a built-in (primitive) rational data type to represent rational numbers like 1/3 and −11/17 without rounding, and to do arithmetic on them. Examples are the ratio type of Common Lisp , and analogous types provided by most languages for algebraic computation , such as Mathematica and Maple .
All rational numbers are real, but the converse is not true. Irrational numbers (): Real numbers that are not rational. Imaginary numbers: Numbers that equal the product of a real number and the imaginary unit , where =. The number 0 is both real and imaginary.
A fixed-point data type uses the same, implied, denominator for all numbers. The denominator is usually a power of two.For example, in a hypothetical fixed-point system that uses the denominator 65,536 (2 16), the hexadecimal number 0x12345678 (0x1234.5678 with sixteen fractional bits to the right of the assumed radix point) means 0x12345678/65536 or 305419896/65536, 4660 + the fractional ...
A number has a terminating or repeating expansion if and only if it is rational; this does not depend on the base. A number that terminates in one base may repeat in another (thus 0.3 10 = 0.0100110011001... 2). An irrational number stays aperiodic (with an infinite number of non-repeating digits) in all integral bases.
The Stern–Brocot tree forms an infinite binary search tree with respect to the usual ordering of the rational numbers. [1] [2] The set of rational numbers descending from a node q is defined by the open interval (L q, H q) where L q is the ancestor of q that is smaller than q and closest to it in the tree (or L q = 0 if q has no smaller ...
Since every rational number has a unique representation with coprime (also termed relatively prime) and , the function is well-defined. Note that q = + 1 {\displaystyle q=+1} is the only number in N {\displaystyle \mathbb {N} } that is coprime to p = 0. {\displaystyle p=0.}