As long as the initial assumptions in the estimate are reasonable quantities, the result obtained will give an answer within the same scale as the correct result, and if not gives a base for understanding why this is the case. For example, if the estimate tells you there should be a hundred or so tuners but the precise answer tells you there are many thousands then you know you need to find out why there is this divergence from the expected result. First looking for errors, then for factors the estimation didn't take account of - Does Chicago have a number of music schools or other places with a disproportionately high ratio of pianos to people?