Explain uncertainty or error in given asurement by suitable example.

Explanation

Length and breadth of a thin rectangular plate is I = 16.2 cm and breadth b = 10.1 cm
Least count of meterscale is 0.1 cm hence absolute error in measurement should be 0.1 cm.
`l=(16.2+-0.1) cm`
`b=(10.1+-0.1)cm`
% error in measurement of length,
`l=(16.2+-0.6%)`
% error in measurement of breadth
`b=(10.1+1%)` cm
Area of rectangleular plate,
A=lb
`=16.2xx10.1=163. 62cm^(3)`
% error in A :
`=(DeltaA)/(A)xx100=(Deltal)/(l)xx100+(Deltab)/(b)xx100`
`=(0.6%+1%)=1.6%`
`DeltaA=(1.6xx163.62)/(100)=2.6`
Area `:A=(163.62+-2.6) cm^(2)`
Here minimum significant digit are 3 hence area should be represented as,
`A~~163 +- 3 cm^(-2)`
`:.` Error in measurement of area of plate is `3 cm^(2)`
(2) If a set of experimental data is specified to .n. significant figures, a result obtained by combining the data will also be valid to .n significant figures.
However, if data is subtracted the number of significant figures can be reduced.
For example,
`12.9 g - 7.06 g = 5.84 g`
Here, there are 3 significant digits. But in subtraction digit after decimal point are considered hence this will be represented as `5.8 g`
(3) The relative error of a value of number specified to significant figure does not depend on .n. but also to the number itself. For example, in measurement of mass observation is m = 10.2 g then accuracy is `+-0.01g`
`:.` Percentage error in 1.02g
`=+-(Deltam)/(m)xx100%`
`=+-(0.01)/(1.02)xx100%`
`+-(1)/(1.02)%`
`=+-(1)/(1.02)%`
`~~+-1%`
In another example m = 9.89 g inaccuracy is `+-0.01g`
vPercentage error in measurement
`=+-(0.01)/(9.89)xx100%`
`=+-0.1011122%`
`=+-0.1%`
Intermediate result in a multistep computation should be calculated to one more significant figure in every measurement than the number of digits in the least precise measurement.
For example, write reciprocal of 9.58 W.r.t.
significant number `(1)/(9.58)=0.10438413`
By rounding of result to 3 digit we get 0.104. But, if we take reciprocal of 0.104 upto 3 significant digit we get 9.62 and reciprocal of 0.1044 gives us 9.58. Hence, one more extra significant digit is kept in intermediate step of complex multistep calculation in order to avoid additional error in the process of rounding off the numbers.