Rules for logarithm

The calculator will give you a numerically correct answer, but you must consider how many significant figures you need to report based on the original measurements' uncertainty.

For logarithmic quanitites, the number to the left of the decimal point called the characteristic. The number to the right of the decimal point is called the mantissa. When considering the number of significant figures, do not consider the characteristic as it only serves to locate the decimal point of the number. The mantissa has as many significant figures as the measured quanitity.

For example:

pH = -log[H+]

Question: What is the pH of a 0.01023 M HCl solution?

Answer: pH = -log(0.01023) = 1.990124366 = 1.9901 (The 4 significant figures in the answer is shown in red.)

The answer should be reported such that the mantissa has 4 significant figures because the concentration of the HCl solution, 0.01023 M, is given to 4 significant figures. The characteristic is not considered when counting significant figures in a logarithmic quantity.