Editing Fermi problem (section)

==Advantages and scope==
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Scientists often look for Fermi estimates of the answer to a problem before turning to more sophisticated methods to calculate a precise answer. This provides a useful check on the results. While the estimate is almost certainly incorrect, it is also a simple calculation that allows for easy error checking, and to find faulty assumptions if the figure produced is far beyond what we might reasonably expect. By contrast, precise calculations can be extremely complex but with the expectation that the answer they produce is correct. The far larger number of factors and operations involved can obscure a very significant error, either in mathematical process or in the assumptions the equation is based on, but the result may still be assumed to be right because it has been derived from a precise formula that is expected to yield good results. Without a reasonable frame of reference to work from it is seldom clear if a result is acceptably precise or is many degrees of magnitude (tens or hundreds of times) too big or too small. The Fermi estimation gives a quick, simple way to obtain this frame of reference for what might reasonably be expected to be the answer.

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, suppose a person was asked to determine the number of piano tuners in Chicago. 
If their initial estimate told them there should be a hundred or so, but the precise answer tells them there are many thousands, then they know they need to find out why there is this divergence from the expected result. First looking for errors, then for factors the estimation did not take account of – does Chicago have a number of music schools or other places with a disproportionately high ratio of pianos to people? Whether close or very far from the observed results, the context the estimation provides gives useful information both about the process of calculation and the assumptions that have been used to look at problems.

Fermi estimates are also useful in approaching problems where the optimal choice of calculation method depends on the expected size of the answer. For instance, a Fermi estimate might indicate whether the internal stresses of a structure are low enough that it can be accurately described by [[linear elasticity]]; or if the estimate already bears significant relationship in [[Scale (ratio)|scale]] relative to some other value, for example, if a structure will be over-engineered to withstand loads several times greater than the estimate.{{citation needed|date=December 2018}}

Although Fermi calculations are often not accurate, as there may be many problems with their assumptions, this sort of analysis does inform one what to look for to get a better answer. For the above example, one might try to find a better estimate of the number of pianos tuned by a piano tuner in a typical day, or look up an accurate number for the population of Chicago. It also gives a rough estimate that may be good enough for some purposes: if a person wants to start a store in Chicago that sells piano tuning equipment, and calculates that they need 10,000 potential customers to stay in business, they can reasonably assume that the above estimate is far enough below 10,000 that they should consider a different business plan (and, with a little more work, they could compute a rough upper bound on the number of piano tuners by considering the most extreme ''reasonable'' values that could appear in each of their assumptions).