The SI system defines seven base quantities — length (m), mass (kg), time (s), current (A), temperature (K), amount (mol), and luminosity (cd) — from which all other units are derived. Every physical quantity has a unique dimensional formula expressed in terms of M, L, and T; for example, force is [M^{1}$$L^{1}$$T^{-2}] and energy is [M^{1}$$L^{2}$$T^{-2}]. Dimensional analysis can check equation validity, derive functional relationships, and convert units between systems by applying n_{2} = n_{1}($M_{1}$/$M_{2}$)ᵃ($L_{1}$/$L_{2}$)ᵇ($T_{1}$/$T_{2}$)ᶜ. However, dimensional analysis cannot determine dimensionless constants and cannot distinguish between physically different quantities that share the same dimensional formula. Significant figures reflect measurement precision: leading zeros are never significant, while trailing zeros after a decimal point always are. For addition and subtraction, the result is rounded to the fewest decimal places; for multiplication and division, it is rounded to the fewest significant figures. Systematic errors produce consistent deviations from the true value and can be corrected by recalibration, whereas random errors are unpredictable and are reduced only by averaging. Absolute error has the same units as the measured quantity, relative error is dimensionless, and percentage error equals relative error multiplied by 100. For error propagation: add absolute errors for sums/differences; add relative errors for products/quotients; multiply relative error by the power for Z = Aⁿ. Errors never subtract — always add to obtain the maximum (worst-case) uncertainty in any derived quantity.