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.

AccuratePreciseImpreciseInaccurate
Accuracy and precision are independent of each other

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

`"RU" = ("experimental uncertainty")/("measured value") xx 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.