Combination of errors: When a quantity is written in the form of an equation or formula in which the sum, subtraction, multiplication or division of more than one quantity is present, then how is the error affected by such combination of quantities or after the combination We read here the combination of errors to find the value of the total error.
For example, the density of a substance depends on the mass of the substance and its volume, that is, the density of the substance depends on the ratio of the mass and volume of that substance.
D = M/V
Here there is a division between the two quantities, now if there is an error in the measurement of the mass and volume of that substance, then there will be an error in the density of the substance as well. Therefore, it is necessary to know the error in the division of the quantities here.
1. Error accumulation in addition:-
Let two quantities be a and b respectively, which are added and their sum gives the amount x.
Now if there is some error in the measurement of quantities a and b, then there will be an error in the sum of their sum x.
Let the error in a be a and the error in the measurement of b be b. The error in the amount x obtained by the sum of both the quantities is x.
meaning
x = a + b
error in a
error in b b
Error in x x
so
x ± x = (a ± a) + (b ± b)
x ± x = (a + b) ± a ± b
Since we have read above that x = a + b
so
x ± x = x ± a ± b
± x = ± a ± b
That is, the following possible values of errors generated in the sum of the quantities are possible –
(+Δa + b) , (+ a – b) , (- a + b) , (- a – b)
