Units, Scientific Notation, and Significant Figures

Accuracy vs. Precision

In the previous section on significant figures we dealt obliquely with the accuracy of an experiment. In this section we'll deal with the precision of an experiment. In everyday usage the two words have very similar meanings, but in science there meanings are quite different.

Precision is the degree to which the results of multiple repeat experiments agree with one another. For instance if an experiment is repeated 3 times and the same result is obtained all three times, then the result is considered to be very precise. Accuracy is the degree to which the results of an experiment agree with the true or known value.

an experiment or set of experiments may be very precise but not accurate. Less commonly, the results could be accurate but not precise.

An Example

A chemist is asked to determine the concentration of a chemical dissolved in a solution. The chemist performs the experiment three times for good measure, and the concentration determined to be 1.74 M, (moles/liter), 1.73 M and 1.75 M. The average of these numbers is 1.74 M. This result is extremely precise, but suppose the chemist is not a very good chemist and made the same mistake in all three experiments: the true concentration of the chemical in solution is 2.32 M. Even though this experiment was done three times, and the concentration was determined very precisely, it is not an accurate result.

Now let's say that another chemist performs three more experiments to determine the concentration of the same chemical in solution, and finds the following values: 2.87, 1.48 and 2.61 M. When averaged, these values accurately give 2.32 M, but the experiments were not precise. In fact, it may have been lucky that they averaged out perfectly.