(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

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

zeros.

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.

MD0837

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