(2) An alternate method is to express the original number in scientific
notation. The power of ten in the expression is the characteristic of the original number.
The number 20 when expressed in scientific notation is 2.0 X 101. Hence, the
characteristic of the original number is one.
Both methods for determining the characteristic may be used for numbers
less than or greater than one.
b. By Rule.
(1) Original numbers greater than one. If the number whose logarithm is
being determined is greater than one, the characteristic for the logarithm of that number
will be positive and one less than the number of digits found to the left of the decimal
point in the original number. For example:
Number of digits
to left of decimal
(digits - one)
(2) Original numbers that are less than one. If the number whose logarithm
is being determined is less than one, the characteristic for the logarithm of that number
will be negative and is a number one more than the number of zeros to the right of the
decimal point that precede the first nonzero integer. For example:
Number of zeros
to right of decimal
(num. of 0 + 1)
(3) A negative characteristic may be distinguished from a positive
characteristic by placing a negative sign above the characteristic. This is necessary
since the mantissa is always positive. For example:
log 0.2 = 1.3010