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. 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 is
while the number −0.00574012 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.