Q.Find the antilogarithm of 2.6596.

The mantissa gives the significant digits from the antilog table, and the characteristic then fixes where the decimal point goes.

Step 1 — Read the digits from the mantissa. Use only the decimal part, 0.6596, in the antilog table. The row .65, column 9 gives 4560, and the mean-difference column for the fourth digit 6 adds 7, giving the four significant digits $4560 + 7 = 4567$. …

Cross-check by taking the logarithm back. From Worked Example 8, the digit string 4567 has mantissa 0.6596, and 456.7 has 3 digits before the point so characteristic $3-1 = 2$; hence $\log 456.7 = 2.6596$ …

A common error is using the characteristic rather than the mantissa to enter the antilog table, or miscounting the decimal placement — for characteristic 2 the answer has 3 digits before the point, not 2. Always read …