Question
Sat July 28, 2012 By: Manisha
i am not able to understand that how did we get 
     l = 16.2 ± 0.1  cm
= 16.2 cm ± 0.6 %
b = 10.1  ± 0.1 cm
   = 10.1 cm ± 1 %

3 Rules for Determining the Uncertainty in the Resu lts of Ar ithmat ic Calculations The rules for determining the uncertainty or error in the number/measured quantity in arithmetic operations can be understood from the following examples. (1) If the length and breadth of a thin rectangular sheet are measured, using a metre scale as 16.2 cm and, 10.1 cm respectively, there are three significant figures in each measurement. It means that the length l may be written as l = 16.2 ± 0.1 cm = 16.2 cm ± 0.6 %. Similarly, the breadth b may be written as b = 10.1 ± 0.1 cm = 10.1 cm ± 1 % Then, the error of the product of two (or more) experimental values, using the combination of errors rule, will be l b = 163.62 cm2 + 1.6% = 163.62 + 2.6 cm2 This leads us to quote the final result as l b = 164 + 3 cm2 Here 3 cm2 is the uncertainty or error in the estimation of area of rectangular sheet.

Expert Reply
Sun August 05, 2012
If you are not able to understand how we get the percentage error in calculations, it can be easily determined from
A = A ± ?A
 
as percentage error:  ?A/A x 100
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