rational number

Noun

Meaning

an integer or a fraction

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Examples

Applications The fact that any rational number has a unique representation as an irreducible fraction is utilized in various proofs of the irrationality of the square root of 2 and of other irrational numbers. Source: Internet

For example, the division example above is surjective (or onto) because every rational number may be expressed as a quotient of an integer and a natural number. Source: Internet

Any one of these models must be explicitly constructed, and most of these models are built using the basic properties of the rational number system as an ordered field. Source: Internet

Further, for a quadratic polynomial with rational coefficients, it factors over the rationals if and only if the discriminant – which is necessarily a rational number, being a polynomial in the coefficients – is in fact a square. Source: Internet

Given two positive integers their least common multiple and greatest common divisor are given by the formulas : and : Since : this gives : In fact, any rational number can be written uniquely as the product of primes if negative exponents are allowed. Source: Internet

Digital computers, by contrast, must first quantize the signal into a finite number of values, and so can only work with the rational number set (or, with an approximation of irrational numbers). Source: Internet

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