1.5 Precision and Accuracy

1.5 Precision and Accuracy

The terms precision and accuracy are frequently used in physics measurements. They should be distinguished clearly.

The precision of a measurement is determined by the instrument or device being used. The smaller the least count, the more precise is the measurement.

Accuracy is defined as the closeness of a measurement to the exact or accepted value of a physical quantity. It is expressed by the fractional or percentage uncertainty. The smaller the fractional or percentage uncertainty, the more accurate is the measurement.

For example, the length of an object is recorded as $25.5\,\mathrm{cm}$ by using a metre rule having smallest division in millimetre. Its precision or absolute uncertainty (least count) = $\pm 0.1\,\mathrm{cm}$

Fractional uncertainty = $0.1\,\mathrm{cm} / 25.5\,\mathrm{cm}$ = $0.004$

Percentage uncertainty = $(0.1\,\mathrm{cm} / 25.5\,\mathrm{cm}) \times 100\%$ = $0.4\%$

Another measurement taken by Vernier Callipers with least count $0.01\,\mathrm{cm}$ is recorded as $0.45\,\mathrm{cm}$. It has precision or absolute uncertainty (least count) = $\pm 0.01\,\mathrm{cm}$

Fractional uncertainty = $0.01\,\mathrm{cm} / 0.45\,\mathrm{cm}$ = $0.02$

Percentage uncertainty = $(0.01\,\mathrm{cm} / 0.45\,\mathrm{cm}) \times 100\%$ = $2\%$

Thus, the reading $25.5\,\mathrm{cm}$ taken by metre rule is although less precise but is more accurate having less percentage uncertainty or error.

Whereas the reading $0.45\,\mathrm{cm}$ taken by Vernier Callipers is more precise but is less accurate. In fact, it is the relative measurement which is important. The smaller a physical quantity, the more precise instrument should be used. Here the measurement $0.45\,\mathrm{cm}$ demands that a more precise instrument, such as micrometer screw gauge, with least count $0.001\,\mathrm{cm}$, should have been used.

Hence, we can conclude that:

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A precise measurement is the one which has less precision or absolute uncertainty and an accurate measurement is the one which has less fractional or percentage uncertainty.

We can never make an exact measurement. The best we can do is to come as close as possible within the limitation of the measuring instrument.