# Measurements

## Accuracy and precision

Measurements are never *exact*. There is always some uncertainty, usually due to limitations in the measuring instrument or in the human senses.

Accuracy is the closeness of a measurement to the actual value. Precision is the closeness of multiple measurements to each other. For example, a ruler that has more divisions will give you a more precise answer, but not necessarily a more accurate one.

## Uncertainty

Uncertainty is the amount that a particular measurement could be off by. It can be expressed as *absolute* uncertainty, like (20.4 ± 0.3) kg, or as *relative* uncertainty, like 20.4 kg ± 1.5%. Relative uncertainty can be calculated from absolute uncertainty with

$\displaystyle \text{RU} = \frac{\text{experimental uncertainty}}{\text{measured value}} \times 100 \%$.

When adding or subtracting measurements, add up the *absolute* uncertainties. When doing anything else (multiplication, division, square root, etc.), add up the *relative* uncertainties.