I'm assuming you have a table of 4-figure antilogarithms to base 10 with numbers 01 to 99 down the left hand column, and 1-9 across the top of the main columns, with a further 9 narrower columns headed 1-9 to the right of these. The right hand columns are known as 'proportional parts' or 'differences'.
You want to find antilog(0.1204).
For the moment, ignore the number 0 to the left of the decimal point (known as the 'characteristic'). The table deals only with the decimal portion .1204 (known as the 'mantissa').
Look down the left hand column of the table for 12 and find the table entry under the column headed 0 (that's the 3rd. digit in your number). Keep your finger on that number (1.318), and read the number (1) on the same line under 4 (the last digit of your number) in the columns on the right. Add the 1 on to the 1.318 giving 1.319 as the antilogarithm of 0.1204.
As the integer part is 0, in this case you have finished.
If the integer part of the log is a positive number, that is the power of 10 for the multiplier. Antilog(3.1204) would be 1.319 * 10^3.
When using tables of logs and antilogs, it is customary to keep the decimal portion of the log positive. A log which appears as - 1.8796 on a calculator would be written [bar 2].1204. The bar is a minus sign written above the number 2, and applies only to the integer part of the log. The antilog for [bar 2].681 is 1.319 * 10^(-2).
