Units, Measurements & Errors — Core NEET Facts — Summary

The SI system defines 7 base units: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), candela (cd).
All other units are derived from these seven by multiplication/division — no additional base units are needed.
Dimensional formula of force: [ $M^{1}$$L^{1}$$T^{-2}$ ]; energy: [ $M^{1}$$L^{2}$$T^{-2}$ ]; pressure: [ $M^{1}$$L^{-1}$$T^{-2}$ ]; power: [ $M^{1}$$L^{2}$$T^{-3}$ ]; angular momentum: [ $M^{1}$$L^{2}$$T^{-1}$ ]; viscosity: [ $M^{1}$$L^{-1}$$T^{-1}$ ].
The three uses of dimensional analysis: (1) check equation correctness, (2) derive unknown formulas, (3) convert units between systems.
The two limitations of dimensional analysis: (1) cannot determine dimensionless constants like 1/2 or 2π; (2) cannot distinguish formulas with identical dimensions.
Significant figures: leading zeros are never significant; trailing zeros after a decimal are always significant; ambiguous trailing zeros (no decimal) are best expressed in scientific notation.
In addition/subtraction, match decimal places. In multiplication/division, match significant figures.
Systematic errors: consistent direction, correctable by recalibration. Random errors: unpredictable direction, reduced by averaging.
Error propagation: for Z = A ± B → $\Delta Z$ = $\Delta A$ + $\Delta B$ ; for Z = AB or A/B → $\Delta Z$ /Z = $\Delta A$ /A + $\Delta B$ /B; for Z = Aⁿ → $\Delta Z$ /Z = n·( $\Delta A$ /A).
Errors never subtract — always add (worst-case estimation).
For unit conversion: n_{2} = n_{1} × ( $M_{1}$ / $M_{2}$ )ᵃ × ( $L_{1}$ / $L_{2}$ )ᵇ × ( $T_{1}$ / $T_{2}$ )ᶜ where a, b, c are powers in the dimensional formula.
G in CGS: $6.67 \times 10^{-8}$ dyne $cm^{2}$ $g^{-2}$ , converted from $6.67 \times 10^{-1}$ ^{1} N $m^{2}$ $kg^{-2}$ in SI using [ $M^{-1}$$L^{3}$$T^{-2}$ ].
Percentage error = ( $\Delta Z$ /Z) × 100%; for Z = AᵃBᵇ/Cᶜ: % error = a(%A) + b(%B) + c(%C).
Torque and energy share [ $M^{1}$$L^{2}$$T^{-2}$ ]; pressure, stress, and energy density share [ $M^{1}$$L^{-1}$$T^{-2}$ ] — these same-dimension pairs are classic NEET traps.
Dimensionally correct ≠ physically correct: KE = $mv^{2}$ is dimensionally correct but the true formula is ½ $mv^{2}$ .