Units, Measurements & Errors — Common Errors and Misconceptions — Summary

Misconception 1 — Subtracting errors in division: For Z = A/B, many students write $\Delta Z$ /Z = $\Delta A$ /A − $\Delta B$ /B. This is wrong. Relative errors always add: $\Delta Z$ /Z = $\Delta A$ /A + $\Delta B$ /B. The correct answer for a 3%/2% split gives 5%, not 1%.
Misconception 2 — Dimensional correctness confirms physical correctness: Dimensional analysis is a necessary but not sufficient test. KE = $mv^{2}$ passes dimensional analysis but is physically incorrect by a factor of 2. Always treat dimensional correctness as a filter, not a proof.
Misconception 3 — Leading zeros count as significant figures: In 0.00340, the zeros before 3 are placeholders indicating decimal position. Only 3, 4, and 0 (after the last non-zero digit) are significant — 3 sig figs total.
Misconception 4 — Averaging removes systematic error: Averaging only reduces random error. Systematic errors shift all readings in the same direction; their mean is still offset from the true value. Only recalibration or correction factors fix systematic errors.
Misconception 5 — 1500 has 4 significant figures: Without a written decimal point, trailing zeros in integers are ambiguous. Use scientific notation to be explicit: $1.5 \times 10^{3}$ (2 sig figs), $1.50 \times 10^{3}$ (3 sig figs), $1.500 \times 10^{3}$ (4 sig figs).
Misconception 6 — Same dimensions means same physical quantity: Pressure and energy density both have [ $M^{1}$$L^{-1}$$T^{-2}$ ]; torque and energy both have [ $M^{1}$$L^{2}$$T^{-2}$ ]. Dimensions describe mathematical form, not physical content.
Misconception 7 — Decimal-place rule applies to multiplication: For 3.14 × 2.0, some students retain 2 decimal places (6.28). The correct rule for multiplication is to match significant figures: 2 sig figs gives 6.3.
Misconception 8 — The pendulum constant k can be found dimensionally: T = k√(L/g) is derived dimensionally, but k = 2π is dimensionless and completely inaccessible to dimensional analysis.