Combination of error

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Error of a sum or a difference

• If there is two quantities A and B . A can be represented in A士ΔA and B can be represented in B士ΔB then a third quantity Z whose value is A+B
• Z=Z士ΔZ=(A士ΔA)+(B士ΔB)
• 士ΔZ=士ΔA士ΔB
• The maximum value of ΔZ is ΔA+ΔB

Error of a product or quotient

• If there is two quantities A and B . A can be represented in A士ΔA and B can be represented in B士ΔB then a third quantity Z whose value is AB
• Z=Z士ΔZ=(A士ΔA)(B士ΔB)

             Z士ΔZ=AB士BΔA士AΔB士ΔAΔB

Dividing LHS by Z and RHS by AB

            1士(ΔZ/Z)=1士(ΔA/A)士(ΔB/B)士(ΔA/A)(ΔB/B)

            (ΔA/A)(ΔB/B)⋍0

          ΔZ/Z=(ΔA/A)士(ΔB/B)

Hence the maximum relative error is 

           ΔZ/Z=(ΔA/A)+(ΔB/B)

• If there is two quantities A and B . A can be represented in A士ΔA and B can be represented in B士ΔB then a third quantity Z whose value is A/B
• Z=Z士ΔZ=(A士ΔA)/(B士ΔB)
• (Z士ΔZ)(B士ΔB)=A士ΔA
• ZB士ΔZB士ΔZΔB士ΔBZ=A士ΔA
• Dividing LHS by ZB and RHS by A.