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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, d 0 , d 1 , d 2 , d 3 , … , {\textstyle d_{0},d_{1},d_{2},d_{3},\ldots ,} are the digits of the number in base 10, and d 0 {\displaystyle d_{0}} 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 × 10 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.