Fundamental SI Units & Dimensions
Seven fundamental base quantities: Length ($[L]$, meter), Mass ($[M]$, kg), Time ($[T]$, s), Electric Current ($[A]$, Ampere), Thermodynamic Temperature ($[K]$, Kelvin), Amount of Substance ($[mol]$, mole), Luminous Intensity ($[cd]$, Candela).
Principle of Homogeneity of Dimensions:
According to this principle, a physical equation is dimensionally correct if dimensions of all terms on both sides are identical:
$$[L.H.S.] = [R.H.S.]$$
Error Propagation Formulas:
If $Z = \frac{A^p B^q}{C^r}$, then relative error:
$$\frac{\Delta Z}{Z} = p\left(\frac{\Delta A}{A}\right) + q\left(\frac{\Delta B}{B}\right) + r\left(\frac{\Delta C}{C}\right)$$
