Uses:

1. Check correctness of formulae — if dimensions of LHS ≠ RHS, the equation is definitely wrong
2. Derive relations — express a quantity in terms of its dependent variables and equate dimensions
3. Convert units — $n_2$ = $n_1$ * $\frac{M_1}{M_2}$^a * $\frac{L_1}{L_2}$^b * $\frac{T_1}{T_2}$^c

Limitations:

1. Cannot find dimensionless constants (like 1/2, pi, e)
2. Cannot distinguish between quantities with same dimensions (work vs torque)
3. Cannot handle logarithmic, exponential, or trigonometric functions (their arguments must be dimensionless)
4. Cannot derive relations involving more than 3 unknowns with only 3 base dimensions (for mechanics)
5. If a quantity depends on a dimensionless combination, dimensional analysis fails