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There are a couple of well-known algorithms to find the best rational approximation to a given real number. A good and short book is "Diophantine Approximations" by I. Niven. For code, you can also check out this repo of mine: https://github.com/alidasdan/best-rational-approximation .

Note that decimal numbers represented as a floating point numbers on a computer are actually rational numbers due to limited precision. So converting decimal numbers to fractions, both stored on a computer, means converting a fraction with potentially large numerator and/or denominator to a simpler fraction, say, one with a far smaller denonimator.

For example, an approximation to pi is 3.14159265358979323844, which is the same thing as 314159265358979323844/10^20 (trivial approximation). Using these algorithms we can covert this fraction to a simpler fraction under different approximation criteria such as a bound on the approximation error or a bound on the magnitude of the denominator. For this example, we then get various approximations to pi such as 22/7, 355/113, ...