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By default, the output value is rounded to adjust its precision to match that of the input. An input such as 1234 is interpreted as 1234 ± 0.5, while 1200 is interpreted as 1200 ± 50, and the output value is displayed accordingly, taking into account the scale factor used in the conversion.
An equivalent definition is sometimes useful: if a and b are integers, then the fraction a / b is irreducible if and only if there is no other equal fraction c / d such that | c | < | a | or | d | < | b |, where | a | means the absolute value of a. [4] (Two fractions a / b and c / d are equal or equivalent if and ...
A simple fraction (also known as a common fraction or vulgar fraction, where vulgar is Latin for "common") is a rational number written as a/b or , where a and b are both integers. [9] As with other fractions, the denominator (b) cannot be zero. Examples include 1 / 2 , − 8 / 5 , −8 / 5 , and 8 / −5
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 ...
In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator. [1]
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By considering the complete quotients of periodic continued fractions, Euler was able to prove that if x is a regular periodic continued fraction, then x is a quadratic irrational number. The proof is straightforward. From the fraction itself, one can construct the quadratic equation with integral coefficients that x must satisfy.