# Measurement Uncertainty

## Precision and Accuracy

When we make a measurement in the laboratory we need to know how good it is. To this end, we introduce two concepts: Precision and Accuracy.

Precision indicates degree of reproducibility of a measured number, and
Accuracy indicates how close your measurements are to the true value.

Let's look at throwing darts and trying to hit the bullseye as an illustration of these two concepts.

When you make measurements in science you want them to be both precise and accurate.

Two students, Raffaella and Barbara, measured the temperature of boiling water, which by definition should be 100°C under 1 atmosphere of pressure. Each student made 10 temperature measurements, shown below as red (Raffaella) and blue (Barbara) dots.

The average of Raffaella's temperature measurements is 100.1°C and the average of Barbara's is also 100.1°C. So, the accuracy of their measurements is identical. On the other hand, you can see from the figure that the precision of Raffaella's measurements was better than Barbara's. The way this is expressed in science is to include an uncertainty with measured values. In this case Raffaella would report a boiling point of 100.1 ± 0.3°C, and Barbara would report 100.1 ± 1.4°C. This uncertainty is also called a random error, and is different from a systematic error, which is the difference between the average value and the true value. Here, both Raffaella and Barbara had systematic errors of 0.1°C, since the true boiling point of water is 100°C.

• Precision and Accuracy:

If, for whatever reason, the measurement uncertainty cannot be specified, then at the very least, the precision in a measured number can be approximately specified through the number of significant figures. In the example above, Rafaella would report a boiling point of 1.001 x 102 °C, whereas Barbara would report 1.00 x 102 °C. That is, Rafaella's result has four significant figures while Barbara's has only three.