Coefficient

In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series or any expression; it is usually a number, but in any case does not involve any variable of the expression. For instance in

the first two terms respectively have the coefficients 7 and −3. The third term 1.5 is a constant. The final term does not have any explicitly written coefficient, but is considered to have coefficient 1, since multiplying by that factor would not change the term. Often coefficients are numbers as in this example, although they could be parameters of the problem or any expression in these parameters. In such a case one must clarify which symbols represent variables and which ones represent parameters. Following Descartes, the variables are often denoted by x, y, ..., and the parameters by a, b, c, ..., but it is not always the case. For example, if y is considered as a parameter in the above expression, the coefficient of x is −3y, and the constant coefficient is 1.5 + y.

Coefficient (disambiguation)

Coefficient could have one of the following meanings:

Also,

Significand

The significand (also mantissa or coefficient) is part of a number in scientific notation or a floating-point number, consisting of its significant digits. Depending on the interpretation of the exponent, the significand may represent an integer or a fraction. The word mantissa seems to have been introduced by Arthur Burks in 1946 writing for the Institute for Advanced Study at Princeton, although this use of the word is discouraged by the IEEE floating-point standard committee as well as some professionals such as the creator of the standard William Kahan.

Example

The number 123.45 can be represented as a decimal floating-point number with the integer 12345 as the significand and a 10⁻² power term also called characteristics, where −2 is the exponent (and 10 the base). Its value is given by the following arithmetic:

This same value can also be represented in normalized form with 1.2345 as the fractional coefficient, and +2 as the exponent (and 10 as the base):

Schmid, however, called this representation with a significand ranging between 1.0 and 10 a modified normalized form.