# Error in sum of the quantities

Suppose

*x*=*a*+*b*, i.e., sum of*a*and*b*.Let

Î”

*a*= absolute error in measurement of*a*Î”

*b*= absolute error in measurement of*b*Î”

*x*= absolute error in calculation of*x*Maximum absolute error in

*x*is Î”*x*= Â±(Î”*a*+ Î”*b*)Percentage error in the value of

# Error in difference of the quantities

Suppose

*x*=*a*â€“*b*Let

Î”

*a*= absolute error in measurement of*a*Î”

*b*= absolute error in measurement of*b*Î”

*x*= absolute error in calculation of*x*, i.e., difference of*a*and*b*.Maximum absolute error in

*x*is Î”*x*= Â±(Î”*a*+ Î”*b*)Percentage error in the value of

*x*is# Error in product of quantities

Suppose

*x*=*a*Ã—*b*Let

Î”

*a*= absolute error in measurement of*a*,Î”

*b*= absolute error in measurement of*b*Î”

*x*= absolute error in calculation of*x*, i.e., product of*a*and*b*.Maximum fractional error in

*x*isPercentage error in the value of

*x*= (% error in value of

*a*) + (% error in value of*b*)# Error in division of quantities

Suppose

*x*=*a*/*b*Let

Î”

*a*= absolute error in measurement of*a*,Î”

*b*= absolute error in measurement of*b*Î”

*x*= absolute error in calculation of*x,*i.e.,division of*a*and*b*.Maximum fractional error in

*x*isPercentage error in the value of

*x*= (% error in value of

*a*) + (% error in value of*b*)# Error in quantity raised to some power

Suppose

*x*=*a*/^{n}*b*^{m}.Let

Î”

*a*= absolute error in measurement of*a*,Î”

*b*= absolute error in measurement of*b*Î”

*x*= absolute error in calculation of*x*The maximum fractional error in

*x*isPercentage error in the value of

*x*=

*n*(% error in value of*a*) +*m*(% error in value of*b*)# Some Important Applications

- For a simple pendulum,
- For a sphere
- When two resistors
*R*_{1}and*R*_{2}are connected*R*=_{s}*R*_{1}+*R*_{2}*R*= Î”_{s}*R*_{1}+ Î”*R*_{2}_{}_{In parallel,}_{}_{}â‡’