floating-point number

A number expressed as a mantissa value qualified by an exponent value, e.g. (0.123 456,-4) to mean 0.123 456 × 10^-4 else 0.123 456 × 16^-4, etc., depending on the implied radix, i.e. numbers in which the true value is obtained by floating the decimal (or equivalent) point the indicated number of places, four to the left in the above example, producing 0.000 0123 456 if with a decimal radix. With normalization of the mantissas to an appropriate set range (typically to the highest arithmetic value less than 1, as illustrated here), this notation allows retention, within a fixed amount of space, of comparable numeric significance over a wide range of numeric size. In external display, it is usual to adopt decimal radix and the convention of using E preceding the exponent, e.g. 0.987 6 E + 12 to mean 0.987 6 × 10¹².