PRECISION AND ACCURACY

PRECISION

Definition:

A precise measurement is the one which has less precision or absolute uncertainty. Or

An accurate measurement is the one which has less fractional or percentage uncertainty or error.

Explanation:

The precision of a measurement is determined by the instrument or device being used. The accuracy of a measurement depends upon the fractional or percentage uncertainty in that measurement.

Example:

When the length of an object is recorded as 25.5 cm by using a meter rod having smallest division in millimeter, it is the difference of two readings of the initial and final positions, The uncertainty in the single reading as described in the previous example is taken as ±0.05 cm which is now doubled (due to initial and final readings) is called “absolute uncertainty”.

Thus absolute uncertainty =±0.05±0.05 = ±0.1 cm.

The absolute uncertainty is equal to least count of the measuring instrument i.e. meter rod. This is called precision.

First Case:

Precision or absolute uncertainty (least count) = ± 0.1 cm.

As the length of the object recorded by a meter rod having least count 0.1 cm is 25.5 cm. Then fractional uncertainty = 0.1cm/25.5cm = 0.004

Percentage uncertainty = 0.1/25.5 x 100/100 = 0.4/100 = 0.4%

 

Second Case

Another measurement of length is taken by vernier caliper with least count as 0.01 cm is recorded as 0.45 cm it has Precision or absolute uncertainty (least count) = ± 0.01 cm

Fractional uncertainty = 0.01cm / 0.45cm = 0.02cm

Percentage uncertainty = 0.01/0.45 x 100/100 = 2/100 = 2.0%

This shows that the reading 25.5 cm taken by meter rod is less precise but is more accurate. In fact, it is the relative measurement, which is important. The smaller a physical quantity, the more precise instrument should be utilized. Thus the measurement 0.45 cm demands that a more precise instrument such as micrometer screw gauge with least count 0.001 cm should be utilized.