Cornell Notes — Subtopic: Error Propagation — Notes

Cue / Question	Notes
What is absolute error?
What is relative error?	$\Delta A$ /A — dimensionless ratio
What is percentage error?	( $\Delta A$ /A) × 100%
Z = A + B → error?	$\Delta Z$ = $\Delta A$ + $\Delta B$
Z = A − B → error?	$\Delta Z$ = $\Delta A$ + $\Delta B$ (still add, never subtract)
Z = A × B → error?	$\Delta Z$ /Z = $\Delta A$ /A + $\Delta B$ /B
Z = A / B → error?	$\Delta Z$ /Z = $\Delta A$ /A + $\Delta B$ /B (same as multiply)
Z = $A^{2}$ → % error?	2 × (% error in A)
Z = $A^{2}$ × B / $C^{3}$ → % error?	2(%A) + 1(%B) + 3(%C)

Summary: The golden rule of error propagation: for addition/subtraction use absolute errors; for multiplication/division use relative errors; for powers multiply the relative error by the exponent. You never subtract errors — always add. This guarantees worst-case (maximum) error estimation.