Scientific Notation - Normalized Notation

Normalized Notation

Any given number can be written in the form of a×10^b in many ways; for example, 350 can be written as 3.5×102 or 35×101 or 350×100.

In normalized scientific notation, the exponent b is chosen so that the absolute value of a remains at least one but less than ten (1 ≤ |a| < 10). Following these rules, 350 would always be written as 3.5×102. This form allows easy comparison of two numbers of the same sign in a, as the exponent b gives the number's order of magnitude. In normalized notation, the exponent b is negative for a number with absolute value between 0 and 1 (e.g., negative one half is written as −5×10−1). The 10 and exponent are usually omitted when the exponent is 0. Note that 0 cannot be written in normalized scientific notation since it cannot be expressed as a×10^b for any non-zero a.

Normalized scientific form is the typical form of expression of large numbers for many fields, except during intermediate calculations or when an unnormalised form, such as engineering notation, is desired. Normalized scientific notation is often called exponential notation—although the latter term is more general and also applies when a is not restricted to the range 1 to 0 (as in engineering notation for instance) and to bases other than 10 (as in 315× 2^20).