(4) Equivalently, the negative logarithm of 0.2 could be expressed as the
difference between the characteristic and mantissa. This is done to facilitate certain
methods of calculation, pH in particular. In this case, the negative sign is placed in front
of the difference. For example:
log 0.2 = 1.3010 = 0.3010 - 1 = -0.6990
This method is considered by most authors to be an incorrect method to express the
logarithm of a number less than one because the mantissa may never be negative.
However, this method is commonly used by electronic calculators and certain other
methods of calculation. You should be able to use either method without error in the
laboratory, as long as you consistently use either approach.
(5) A logarithm with a negative characteristic may also be changed to a
positive form by adding ten to the characteristic and adding minus (-) ten after the
mantissa. Since ten is both added and subtracted to the logarithm the operation does
not change the value of the logarithm. For example:
log 0.2 = 1.3010
Add ten to the characteristic
10 + (-1) = 9 ----> 9.3010
Add minus ten (-10) after the mantissa
9.3010 - 10 = 1.3010
1-35. DETERMINATION OF THE MANTISSA
The mantissa of the logarithm is found in the table of "common" logarithms (see
Appendix B) and is independent of the position of the decimal point in the original
number. Thus, the numbers 0.02, 0.2, 2, 20, 200, 2,000, and 20,000 all have the same
mantissa; i.e., 0.3010.
a. In determining the number to obtain the mantissa, do not consider preceding
b. The number for which a mantissa is desired, commonly referred to as the
natural number, must contain at least three digits, the last two of which may be zeros.
c. For numbers that contain less than three digits, add enough zeros to yield a
three digit number.