Question

Show that the maximum error in the quotient of two quantities is equal to the sum of their individual
fractional errors.​

Answer 1

suppose

• Z=X+Y..........(1)

then , final value of Z is

• Z=(X + ∆X) + (Y + ∆Y)
• where ∆x and ∆Y are the maximum possible of errors in X and Y respectively.

If maximum possible errors in Z is + ∆Z then,

• Z + ∆Z=(X + ∆X) + (Y + ∆Y)
• =[X+Y] + (∆X + ∆Y)

• or, ∆Z=∆X + ∆Y

therefore the maximum possible errors in the final value is the sum of individual absolute errors.