Normalized number

In applied mathematics, a number is normalized when it is written in scientific notation with one non-zero decimal digit before the decimal point. Thus, a real number, when written out in normalized scientific notation, is as follows: : \pm d_0 . d_1 d_2 d_3 \dots \times 10^n where n is an integer, d_0, d_1, d_2, d_3, \ldots, are the digits of the number in base 10, and d_0 is not zero. That is, its leading digit (i.e., leftmost) is not zero and is followed by the decimal point. Simply speaking, a number is normalized when it is written in the form of a × 10 n where 1 ≤ |a| < 10 without leading zeros in a. This is the standard form of scientific notation. An alternative style is to have the first non-zero digit after the decimal point.

In applied mathematics, a number is normalized when it is written in scientific notation with one non-zero decimal digit before the decimal point. Thus, a real number, when written out in normalized scientific notation, is as follows: \pm d_0 . d_1 d_2 d_3 \dots \times 10^n where n is an integer, d_0, d_1, d_2, d_3, \ldots, are the digits of the number in base 10, and d_0 is not zero. That is, its leading digit (i.e., leftmost) is not zero and is followed by the decimal point. Simply speaking, a number is normalized when it is written in the form of a × 10 n where 1 ≤ |a| 9.18082 \times 10^2, while the number in normalized form is -5.74012 \times 10^{-3}. Clearly, any non-zero real number can be normalized. ==Other bases== The same definition holds if the number is represented in another radix (that is, base of enumeration), rather than base 10. In base b a normalized number will have the form \pm d_0 . d_1 d_2 d_3 \dots \times b^n, where again d_0 \neq 0, and the digits, d_0, d_1, d_2, d_3, \ldots, are integers between 0 and b - 1 . In many computer systems, binary floating-point numbers are represented internally using this normalized form for their representations; for details, see normal number (computing). Although the point is described as floating, for a normalized floating-point number, its position is fixed, the movement being reflected in the different values of the power. ==See also== Significand Normal number (computing) ==References==

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