The logarithm of a number consists of two parts. The integral part is known as the characteristic and the decimal part is called the mantissa.

For example, in log₁₀ 200 = 2.3010, the integral part is 2 and the decimal part is 0.3010; therefore, characteristic = 2 and mantissa = 0.3010.

It should be remembered that the mantissa is always written as positive.

To make the mantissa positive (in case the value of the logarithm of a number is negative) subtract 1 from the integral part and add 1 to the decimal part.

Thus, \(- 3.4328 =  - (3 + .4328) = - 3 - 0.4328\)

\(= (- 3 - 1) + (1- 0.4328) = - 4 + .5672  =  \overline 4 .5672\)

So the mantissa is  \(.5672\)

The characteristic may be positive or negative, if it is negative; it is represented by putting a bar on the number. Thus instead of – 4, we should write \(\overline 4 \). Hence we may write \(- 4 + .5672\) as \(\overline 4 .5672\).

Example 1: Find by inspection the characteristics of the logarithms of 21735, 23.8, 350, 0.035, 0.2, 0.87, 0.875.

Solution: Characteristic of logarithm 21735 will be 4.

Number of digits are 5, hence subtracting 1 from the number of digits, we will get characteristic = 4.

Characteristic of logarithm 23.8 will be 1.

Characteristic of logarithm 350 will be 2.

Characteristic of logarithm .035 will be – 2.

(adding one to the number of ciphers immediately after decimal).  

Characteristic of logarithm .2 will be – 1

Characteristic of logarithm .87 will be – 1

Characteristic of logarithm .875 will be – 1