I ran across this quote from John Tukey a couple days ago:
An approximate answer to the right problem is worth a good deal more than an exact answer to an approximate problem.
Too often approximate problems take on a life of their own and we forget that they were approximations. We worry about numerical results to many significant figures when the original model might be doing well to get within 20% of reality. Better to produce a crude solution to a more realistic problem. As G. K. Chesterton said, anything worth doing is worth doing poorly.
On the other hand, you’ll probably face less criticism if you produce exact solutions to unrealistic problems than if you produce approximate solutions to realistic problems. At least that’s what I’ve seen. I suppose this is because it takes less understanding to find fault with your solution than to evaluate your choice of problem to solve.