Cleaning up decimal numbers
Python 3, 66 61 bytes

lambda x:Fraction(x).limit_denominator
from fractions import*

Try it online!
The above function takes a floating point number and returns a bound function Fraction.limit_denominator which, in turn, takes the upper bound for the denominator to return a simplified, approximated fraction as requested.
As you can tell, I’m more of an API reader than a golfer.


minus 5 bytes thanks to ovs