The idea of compatible numbers is to get close to the true answer quickly, because you can do this quick estimation in your head with little effort. When you spend a little time getting the accurate answer, the quick estimation has already told you roughly what answer to expect. If your accurate answer is way off the estimation, you may have made a mistake, and you will then look closer to see why the answer is so different from what you expected. So, to summarise, a quick estimate in your head before tackling a problem in more depth gives you an idea of what to expect and your confidence is boosted when you do the proper calculation and discover that the true answer and the estimate are close.