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Exponentiation with negative exponents is defined by the following identity, which holds for any integer n and nonzero b: =. [1] Raising 0 to a negative exponent is undefined but, in some circumstances, it may be interpreted as infinity (). [22]
An irrational fraction is one that contains the variable under a fractional exponent. [12] An example of an irrational fraction is / / /. The process of transforming an irrational fraction to a rational fraction is known as rationalization.
If K is a field (such as the complex numbers), a Puiseux series with coefficients in K is an expression of the form = = + / where is a positive integer and is an integer. In other words, Puiseux series differ from Laurent series in that they allow for fractional exponents of the indeterminate, as long as these fractional exponents have bounded denominator (here n).
A fixed-point representation of a fractional number is essentially an integer that is to be implicitly multiplied by a fixed scaling factor. For example, the value 1.23 can be stored in a variable as the integer value 1230 with implicit scaling factor of 1/1000 (meaning that the last 3 decimal digits are implicitly assumed to be a decimal fraction), and the value 1 230 000 can be represented ...
The positive and negative normalized numbers closest to zero (represented with the binary value 1 in the exponent field and 0 in the fraction field) are ±1 × 2 −126 ≈ ±1.17549 × 10 −38 The finite positive and finite negative numbers furthest from zero (represented by the value with 254 in the exponent field and all 1s in the fraction ...
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 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]
The most direct method of calculating a modular exponent is to calculate b e directly, then to take this number modulo m. Consider trying to compute c, given b = 4, e = 13, and m = 497: c ≡ 4 13 (mod 497) One could use a calculator to compute 4 13; this comes out to 67,108,864.