Error Analysis — Common Mistakes — Notes

#	Mistake	Why Wrong	Correction
1	Subtracting errors for Z = A − B	Errors represent uncertainty, never cancel	$\Delta Z$ = $\Delta A$ + $\Delta B$ (always add absolute errors)
2	Subtracting relative errors for Z = A/B	Division does not reduce error in measurement	$\Delta Z$ /Z = $\Delta A$ /A + $\Delta B$ /B (add relative errors)
3	Saying dimensional analysis proves an equation is correct	Confirms dimensional consistency only	Dimensionally correct ≠ physically correct
4	Counting leading zeros as significant	Leading zeros are placeholders, not measurements	0.00450 → 3 sig figs (4, 5, 0)
5	Ignoring trailing zero after decimal	Trailing zeros after decimal show precision	2.300 → 4 sig figs
6	Assuming same dimensions = same formula	Many different formulas share same dimensions	KE and PE both [ $M^{1}$$L^{2}$$T^{-2}$ ] but are different quantities
7	Applying decimal-place rule to multiplication	Decimal-place rule is for addition/subtraction only	For multiplication: use sig-fig rule
8	Forgetting to multiply relative error by the power	Power rule is: n × ( $\Delta A$ /A), not just $\Delta A$ /A	For Z = $A^{3}$ : $\Delta Z$ /Z = 3 × $\Delta A$ /A
9	Converting G to CGS by only changing mass unit	G has dimensions [ $M^{-1}$$L^{3}$$T^{-2}$ ]; all three must change	Apply full dimensional substitution for all base units
10	Treating ambiguous trailing zeros as significant	1500 without decimal is ambiguous (2, 3, or 4 sig figs)	Use scientific notation: $1.50 \times 10^{3}$ = 3 sig figs