Expressing Results of Chemical Calculations

Two cases are encountered when reporting the results of chemical calculations. If the standard deviations of the values making up the final calculation are known, we then apply the propagation of error methods  and round the results to contain significant digits. However, if we are asked to perform calculations where the precision is indicated only by the significant figure convention, common sense assumptions must be made as to the uncertainty in each number. Finally, the result is rounded so that it contains only significant digits. It is especially important to postpone rounding until the calculation is completed.

At least one extra digit beyond the significant digits should be carried through all of the computations in order to avoid a rounding error. This extra digit is sometimes called a “guard” digit. Modern calculators generally retain several extra digits that are not significant, and the user must be careful to round final results properly so that only significant figures are included. Example 1.1 illustrates this procedure.

Example 1.1

We must emphasize that rounding decisions are an important part of every calculation. These decisions cannot be based on the number of digits displayed on an instrument readout, on the computer screen or on a calculator display.