in the measured volume. Hence the density should be expressed to only significant figures. Density = − . .
Rules for Determining the Uncertainty in the Results of Arithmetic Calculations The rules for determining the uncertainty or error in the number/measured quantity in arithmetic operations can be understood from the following examples. ( ) If the length and breadth of a thin rectangular sheet are measured, using a metre scale as . cm and, . cm respectively, there are three significant figures in each measurement.
It means that the length l may be written as l = . ± . cm = . cm ± .
%. Similarly, the breadth b may be written as b = . ± . cm = .
cm ± % Then, the error of the product of two (or more) experimental values, using the combination of errors rule, will be l b = . cm + . % = . + .
cm This leads us to quote the final result as l b = + cm Here cm is the uncertainty or error in the estimation of area of rectangular sheet. ( ) 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 are subtracted, the number of significant figures can be reduced. For example, .
g – . g, both specified to three significant figures, cannot properly be evaluated as . g but only as . g, as uncertainties in subtraction or addition combine in a different fashion (smallest number of decimal places rather than the number of significant figures in any of the number added or subtracted).
( ) The relative error of a value of number specified to significant figures depends not only on n but also on the number itself. For example, the accuracy in measurement of mass . g is ± . g whereas another measurement .
g is also accurate to ±