Napier thus had complete command over decimal fractions and the use of the decimal point.
The fact that when the base is io the mantissa of the logarithm is independent of the position of the decimal point in the number affords the chief reason for the choice of io as base.
In tables of logarithms of numbers to base io the mantissa only is in general tabulated, as the characteristic of the logarithm of a number can always be written down at sight, the rule being that, if the number is greater than unity, the characteristic is less by unity than the number of digits in the integral portion of it, and that if the number is less than unity the characteristic is negative, and is greater by unity than the number of ciphers between the decimal point and the first significant figure.
The power of io, which occurs as a factor in the tables of both Napier and Byrgius, was rendered necessary by the fact that the decimal point was not yet in use.
A mixed number, the fractional part of which is a decimal fraction, is expressed by writing the integral part in front of the point, which is called the decimal point.