Rev. Notes > AS > Measuring techniques Previous Topic Measuring techniques Next Topic Topics
 Measurements Errors Random error Systematic error Uncertainty Total uncertainity in addition / subtraction Total uncertainty in multiplication and division Total uncertainty in power factor Total uncertainty in the average value of many measurements Total uncertainty in the timing experiment Total uncertainty in the timing experiment Example 1 - Calculation of uncertainty Least count Spring Balance Digital Balance Protractor Micrometer Vernier calliper Digital Ammeter Cathode Ray Osciloscope

## Uncertainty

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 or error.

In measurements made in physics, the terms precision and accuracy are frequently used. They should be distinguished clearly. The precision of a measurement is determined by the instrument or device being used and the accuracy of a measurement depends on the fractional or percentage uncertainty in that measurement.
For example, when the length of an object is recorded as 25.5 cm by using a metre 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 discussed before is taken as ± 0.05 cm which is now doubled and is called absolute uncertainty (least count) =±0.1 cm

Fractional uncertainty = (0.1 cm / 25.5 cm)

Percentage uncertainty = (0.1 cm / 25.5 cm) X (100 / 100) = 0.4 / 100 = 0.4 %

Another measurement taken by vernier calipers 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 = (0.01 cm / 0.45 cm) = 0.02

Percentage uncertainty = (0.01 cm / 0.45 cm) X (100 / 100) = (2.0 / 100) = 2.0 %

Thus the reading 25.5 cm taken by metre rule is although less precise by is more accurate having less percentage uncertainty or error.
Whereas the reading 0.45 cm taken by vernier calipers 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 cm demands that a more precise instrument, such as micrometer screw gauge, with least count 0.001 cm, should have been used. Hence, we can conclude that:

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 or error.

 Yunzila Said : but we have calculated the value with the given radius then what is the need of division by 2......??? 07/12/17 12:21 PM

 Yunzila Said : why in the ans is 0.6.......??? bcz after calculation we get 1.2.....!!! 07/12/17 12:17 PM

 unknown Said : ^to calculate the radius, diameter needs to be divided by 2. thus, 1.22/2 = 0.61 02/01/15 12:33 AM

 Bilal Said : where did 0.6 come from in result 09/09/14 02:51 PM