Significant Figures in Logarithms

The rules for tracking significant figures in logarithm calculations (such as ln or log) are simple, but how you count the digits is a little different. Remember from previously that only the digits in the mantissa of a logarithm are significant – the digits after the decimal:

The same rules apply to “natural logarathims” (ln) as to base-10 logs:

When doing an antilog the same rules apply, but be careful of how you count your significant digits:

Since the exponent in the setup must be the answer to a logarithm, only the digits after the decimal are significant. Therefore we only have two significant digits in our final answer for this calculation (and it is clearest to write in scientific notation).