Combination Of Errors

Combination of error

When we perform the mathematical operations, such as addition, subtraction, division, multiplication etc, the error combination depends on the type of mathematical operation performed on physical quantities.

1. Error In Sum Of Two Quantities

Let ∆A and ∆B be the absolute errors in the two quantities A and B respectively, then

Error in the sum of two quantities
Error in the sum of two quantities

Hence, The maximum possible error in the sum of two quantities is equal to the sum of the absolute errors in the individual quantities.

2. Error In The Difference Of The Two Quantities

We consider the difference Z = A-B, then

Error in the difference of the two quantities
Error in the difference of the two quantities

Hence, the maximum error in the difference of the two quantities is equal to the sum of the absolute error in the individual quantities.

3. Error Of A Product

Let we consider the product Z = AB, then the error ∆Z in Z is given by

Error of a Product
Error of a Product

Hence, the maximum fractional error in the product of two quantities is equal to the sum of the fractional error in the individual quantities.

4. Error In The Division Or Quotient

Let we consider the quotient Z= A/B, then the error ∆Z in Z is given by

Error in the division
Error in the division
Error in the quotient
Error in the quotient

Hence, the maximum fractional error in the quotient of two quantities is equal to the sum of their individual fractional error.

5. Error In The Power Of A Quantities

Error in the Power of a Quantities
Error in the Power of a Quantities
Error in the Power of a Quantities
Error in the Power of a Quantities

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