###### (b) Engineer's thinking: Impact of the factors

- The larger the factors
**P** and **L**, the larger the change in length
- The larger the factors
**E** and **A**, the smaller the change in length
- Hence, the change in length is predicted to be:
**D** = (**P L**)**/**(**A E**)

###### (c) Engineers think of relationship

The relation **D** = (**P L**)**/**(**A E**) connecting 5 parameters **D, P, L, A, E** means that given any 4 parameters, we can determine the fifth one. Textbook writers use this fact to concoct a large number of apparently different problems, involving different materials and situations, but smart students realize that they are all the same relationship. Once realizing that, the smart students move on to a really different problem involving a different relationship.

###### (d) Engineers pay attention to the consistency of units in relations

- This relation A = B + C.D/(E.F) + K/L might make sense if the units of the terms A, B, C.D/(E.F), and K/L are the same.
- Terms such as sin(A), cos(B), exp(C.D/(E.F)) might make sense if A, B, C.D/(E.F) are dimensionless.
- The relation
**D** = (**P L**)/(**A E**) is likely correct because it gives the dimension of length for the change in length **D**; on the other hand, the relation **D** = (**P L**^{2})/(**A E**) is definitely wrong because the resulting unit of D is not length.