# Normalized number

A real number is called normalized, if it is in the form:

$\pm d_0.d_1d_2d_3\dots\times 10^n$

where n is an integer, $d_0,$ $d_1,$ $d_2$, $d_3$... are the digits of the number in base 10, and $d_0$ is not zero.

As examples, the number $x=918.082$ in normalized form is

$9.18082\times10^2$,

while the number −0.00574012 in normalized form is

$-5.74012\times 10^{-3}.$

Clearly, any non-zero real number can be normalized.

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

$\pm d_0.d_1d_2d_3\dots\times b^n,$

where again $d_0\not=0,$ and the "digits" $d_0,$ $d_1,$ $d_2$, $d_3$... are integers between $0$ and $b-1$.

Converting a number to base 2 and normalizing it are the first steps in storing a real number as a floating-point number in a computer.