Characteristic and mantissa

• Logarithm of a number consist of two parts

  Characteristic and Mantissa

Characteristic

• Characteristic is the power of 10 in the scientific notation of a number

• It is the integer part of a logarithm of a number

• It can be both positive and negative

Example#1

• 246.8 is a number find its characteristic

• convert this number to a scientific notation

  $2.468\times 10^{2}$

• Here 2 is the characteristic

Example#2

• 0.00783 is a number find its characteristic

• convert this number to a scientific notation

  $7.83\times 10^{-3}$

• Here -3 is the characteristic and can be notated as $\bar{3}$ as well

Mantissa

• Mantissa is the value find by using log table

• It is the decimal part of a logarithm of a number

• It is always positive

Method of finding mantissa

• First round of the number to 4 digits only i.e. log(43.6789) to 43.68

• Ignore the decimal part of the number i.e. 43.68 to 4368

• First two values represent the row of log table i.e. In 4368, 43rd row

• Third digit represent the column i.e. In 4368, 6th column

• Find the value of intersection of 43 row and 6th column

• Fourth digit represent the column of Mean difference columns i.e 8th column of the mean difference

• Find the value of intersection of 43 row and 8th column of mean difference.

• Add both values and place a decimal point in front of the number

• it will be the mantissa.

Example#1

• Find the mantissa of log(43.254)

Solution:

• First round of = 43.25

• Ignore the decimal point = 4325

• Intersection of 43rd row and 2nd column gives value = 6355

• Intersection of 43rd row and 5th column of mean difference gives value = 5

• Add both = 6355+5=6360

• 0.6360 is our mantissa