Rule 1 — Sum/Difference (Z = A +/- B): Delta(Z) = Delta(A) + Delta(B) (absolute errors add)

Rule 2 — Product/Quotient (Z = A*B or Z = $\frac{A}{B}$): Delta$\frac{Z}{Z}$ = Delta$\frac{A}{A}$ + Delta$\frac{B}{B}$ (relative errors add)

Rule 3 — Power (Z = $A^n$): Delta$\frac{Z}{Z}$ = |n| * Delta$\frac{A}{A}$

Rule 4 — General (Z = $A^p$ * $B^q$ / $C^r$): Delta$\frac{Z}{Z}$ = |p|*Delta$\frac{A}{A}$ + |q|*Delta$\frac{B}{B}$ + |r|*Delta$\frac{C}{C}$

Critical insight: The quantity raised to the highest power contributes the most to the error. If measuring density rho = $\frac{M}{pi*r^2*L}$, the error in r is doubled (power 2) and dominates.