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Characteristic and mantissa

Logarithm of a number contains two parts: characteristic and mantissa. The integral part of the logarithm of a number is called characteristic and the decimal part is called its mantissa. Mantissa is obtained from logarithm tables.

  • For logarithm of numbers greater than 1, characteristic is one less than the number of digits to the left of the decimal.
  • For numbers less than 1, it is one more than the number of zeroes to the right of the decimal, but with a negative sign.
  • Mantissa is always a positive quantity.
  • All numbers lying between 1 and 10, i.e., numbers with 1 digit in the integral part have their logarithms lying between 0 and 1. Therefore, their integral parts are zero only. Similarly, all numbers lying between 10 and 100 have two digits in their integral parts. Their logarithms lie between 1 and 2. Therefore, numbers with two digits have integral parts with 1 as characteristic.

Note: In general, the logarithm of a number containing n digits only in its integral parts is (n – 1) + a fraction.


Example 2.24: log (3000) = 3.4771
Here, 3 is the characteristic and 0.4771 is the mantissa.

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