Explain error of a sum or a difference.

Explanation

Let two physical quantities A and B has measured value `A+-DeltaA and B+- AB` where,
(1) For addition :
Let Z is quantity obtained by addition of A and B.
`:.Z=A+B`
Let error is Z be `DeltaZ`
`Z+-DeltaZ=(A+-DeltaA)+(B+-DeltaB)`
`A+B=Z`
`:. +-Z=+-DeltaA+-DeltaB`
For maximum absolute, error
`DeltaZ = DeltaA+DeltaB`
(ii) For Subtractio n :
Let diference of A and B is Z.
`:.Z=A-B` [ Let `A gt B]` `Z+-DeltaZ=(A+-DeltaA)-(B +-DeltaB)`
`=(A-B)-(+-DeltaA+-DeltaB)`
`A-B=Z`
`+-DeltaZ=+DeltaA+- DeltaB`
For maximum error in Z,
`DeltaZ=DeltaA+DeltaB`
Rule : When two quantities are added or subtracted, the absolute error in the final result is the sum of the absolute errors in the individual quantities.