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 * (M_1/M_2)^a * (L_1/L_2)^b * (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