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, formula_2 are the digits of the number in base 10, and formula_3 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.
Examples.
As examples, the number 918.082 in normalized form is 
while 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 (that is, base of enumeration), rather than base 10. 
In base "b" a normalized number will have the form
where again formula_7 and the digits, formula_2 are integers between formula_9 and formula_10.
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.