Units and measurements form the foundation of physics. The SI system defines seven base quantities: length (m), mass (kg), time (s), current (A), temperature (K), mole (mol), and luminous intensity (cd). All other quantities are derived from these.

Dimensional analysis expresses quantities as [$M^a$ $L^b$ $T^c$ ...]. It serves three purposes: checking equations (both sides must have identical dimensions), deriving relations (equating dimension powers), and converting units. Limitations: cannot find dimensionless constants, cannot distinguish quantities with same dimensions, and cannot handle transcendental functions.

Significant figures indicate measurement precision. Rules: all non-zero digits count, leading zeros don't, trailing zeros after decimal do. In multiplication/division: result has fewest SF. In addition/subtraction: fewest decimal places.

Measuring instruments: Vernier caliper (LC = 0.01 cm typically) and screw gauge (LC = 0.01 mm typically). Zero error correction is essential.

Error analysis: Absolute error = |measured - true|. Relative error = Delta$\frac{x}{x}$. For sums: absolute errors add. For products: relative errors add. For powers: Delta$\frac{Z}{Z}$ = |n|*Delta$\frac{A}{A}$. The variable with the highest power contributes most.