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

## Total uncertainty in power factor

Multiply the percentage uncertainty by that power. For example, in the calculation of the volume of a sphere using %age uncertainty in V = 3 × %age uncertainty in radius r.
As uncertainty is multiplied by power factor, increases the precision demand of measurement. If the radius of a small sphere is measured as 2.25 cm by a vernier callipers with least count 0.01 cm, then
the radius r is recorded as
r = 2.25 ± 0.01 cm
absolute uncertainty = least count = ± 0.01 cm
%age uncertainty in r = (0.01 cm / 2.25 cm) X (100 / 100) = 0.4 %
total percentage uncertainty in V =3 × 0.4 = 1.2%
Thus volume                           V = (4/3) π r3
= (4/3) X 3.14 X (2.25 cm) ³
= 47.689 cm³ with 1.2% uncertainty
Thus the result should be recorded as
V =47.7 ± 0.6 cm³

 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