Numerical methods output decimal numbers that oftentimes result from the division of two (or more) numbers:
- $1.5708... = \frac{\pi}{2}$
- $0.3679... = \frac{1}{e}$
- $0.7071... = \frac{\sqrt2}{2}$
- $0.7501315 ... = \frac{{e}^{\frac{\pi}{12}}}{\sqrt{3}}$ (maybe this one is pushing it a little)
What is a good way to "reverse engineer" a decimal point number to the fraction it might have originated from?
Of course, maintaining a lookup table of values for most commonly encountered decimal numbers and their fractions of "remarkable numbers" is feasible to some extent, but is there a better way?
Side question: what is the proper jargon to succinctly describe this problem?