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:

${\displaystyle \pm d_{0}.d_{1}d_{2}d_{3}\dots \times 10^{n}}$

where n is an integer, ${\textstyle d_{0},d_{1},d_{2},d_{3},\ldots ,}$ are the digits of the number in base 10, and ${\displaystyle d_{0}}$ 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 × 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.