By assigning "dimensions" to various quantities in a consistent manner (using units such as "length", "time", or "mass"), one can provide a simple "checksum" that can be used to guard against numerical errors, particularly with regards to exponents.
Dimensional analysis can also be used as a shortcut to determine various exponents that would come out at the end of a lengthy calculation, without having to directly calculate the exponents in the intermediate steps of the computation.
Use dimensional analysis to predict the dependence of integrals such as or on the underlying parameter or .
(Give solution here...)
Dimensional analysis can be interpreted in terms of an underlying scale invariance of the problem at hand.