Comprehend exact, approximate solutions from "summary" of Comprehending Math by Arthur A. Hyde

Solutions can be exact or approximate depending on how much precision is required. For example, in a business decision involving only a few cents, an approximate result may provide all the accuracy needed and save time.

To find the most accurate solution to a problem, one has to be aware of the differences between exact and approximate answers; different degrees of precision available depend on the requirements and limitations of its use.

Knowing when to use exact solutions versus approximate solutions is important for correctly solving problems. When dealing with physical sciences, exact answers should always be obtained since results from approximations are less reliable.

These days many problems are solved by computers, and there is no need to worry about whether an answer given is exact or approximate. However, it is still important to know which type of solution would best fit the situation faced.

With any problem, one must consider the amount of effort and time spent in pursuit of a solution. Using an approximation can often simplify the calculations leading to the answer and make finishing the problem quicker than if you intended to go through the whole process precisely.

Before beginning any computation, it’s worth evaluating whether or not direct computation is necessary, and if the problem can be estimated instead. Approximate solutions are quicker and simpler, however, sometimes they lead to errors that can be avoided by computed answers.

Estimation skills require an understanding of the context and purpose behind the question and this is key in determining whether to pursue a precise or approximate solution.

It is possible to detect errors in an approximate solution more easily, due to the fact that the outcome lies within a well-defined range of numbers. This simplifies the process compared to detecting errors in exact solutions which could have lots of decimal places.