In mathematics, a rational number is a number that can be expressed as the quotient or fraction ⁠ p q {\displaystyle {\tfrac {p}{q}}} ⁠ of two integers...

In number theory, given a prime number p, the p-adic numbers form an extension of the rational numbers which is distinct from the real numbers, though...

proof that π cannot be rational; Legendre (1794) completed the proof and showed that π is not the square root of a rational number. Liouville (1840) showed...

mathematics, the irrational numbers are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of...

In mathematics, a dyadic rational or binary rational is a number that can be expressed as a fraction whose denominator is a power of two. For example...

Gaussian rational number is a complex number of the form p + qi, where p and q are both rational numbers. The set of all Gaussian rationals forms the...

positive and negative integers. Rational number arithmetic involves operations on fractions of integers. Real number arithmetic is about calculations...

number that it represents. In mathematics, the notion of number has been extended over the centuries to include zero (0), negative numbers, rational numbers...

decimal represents a rational number, the quotient of two integers, if and only if it is a repeating decimal or has a finite number of non-zero digits....

An algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example...

well a real number can be approximated by rational numbers. For this problem, a rational number p/q is a "good" approximation of a real number α if the absolute...

primes or other number-theoretic objects in some fashion (analytic number theory). One may also study real numbers in relation to rational numbers, as for...

finite number of nonzero digits), the decimal is said to be terminating, and is not considered as repeating. It can be shown that a number is rational if...

rational number (for example 2 2 {\displaystyle \textstyle {\frac {\sqrt {2}}{2}}} ), and even do not represent any number (for example the rational fraction...

transcendental number is a real or complex number that is not algebraic: that is, not the root of a non-zero polynomial with integer (or, equivalently, rational) coefficients...

inequality implies that Liouville numbers possess an excellent sequence of rational number approximations. In 1844, Joseph Liouville proved a bound showing that...

representation for a real number is finite if and only if it is a rational number. In contrast, the decimal representation of a rational number may be finite, for...

numbers: typically "0" (zero) and "1" (one). A binary number may also refer to a rational number that has a finite representation in the binary numeral...

Look up rational in Wiktionary, the free dictionary. Rational may refer to: Rational number, a number that can be expressed as a ratio of two integers...

allowing modular division to be transformed into multiplication. Every rational number can be represented as a sum of distinct unit fractions; these representations...

the radial coordinate r given the polar angle θ (though when k is a rational number, a rose curve can be expressed in Cartesian coordinates since those...

containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more...

often, a computer will use a rational approximation to a real number. The most general data type for a rational number (a number that can be expressed as...

mathematics, an algebraic number field (or simply number field) is an extension field K {\displaystyle K} of the field of rational numbers Q {\displaystyle...

of rational numbers Q {\displaystyle \mathbb {Q} } , i.e. 1 Q ( x ) = 1 {\displaystyle \mathbf {1} _{\mathbb {Q} }(x)=1} if x is a rational number and...

fundamental type, so an integer is a rational number and a number, but the converse is not necessarily true, i.e. not every number is an integer. This asymmetry...

which case it is not a normal number). For bases r and s with log r / log s rational (so that r = bm and s = bn) every number normal in base r is normal...

fraction denoting the same rational number 1, the mediant of the fractions 2/2 and 1/2 is 3/4. For a stronger connection to rational numbers the fractions...

A schizophrenic number or mock rational number is an irrational number which displays certain characteristics of rational numbers. It is one of the numerous...

specified rational number ε > 0 representing the desired maximum permissible absolute error, it is algorithmically possible to compute a rational number vapprox...