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:
where n is an integer, are the digits of the number in base 10, and is not zero. That is, its leading digit 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 × 10n 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.
Examples
As examples, the number 918.082 in normalized form iswhile the number in normalized form is
Clearly, any non-zero real number can be normalized.
Other bases
The same definition holds if the number is represented in another radix, rather than base 10.In base b a normalized number will have the form
where again and the digits, are integers between and.
In many computer systems, binary floating-point numbers are represented internally using this normalized form for their representations; for details, see normal number. 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.