Fractions in python returning ridiculously big numbers

Question

I have Python code to solve some recursion and I want it to return some fractions.

The problem is that my code returns ridiculous fractions (which are correct) but they are not the smallest fractions possible, I know it since I can just solve the formula by hand.

Here's my code:

from __future__ import division
import sys
from fractions import Fraction
def t(n):
    if n==0:
        return 0
    else:
        return 1/(4-t(n-1))

print(Fraction(t(int(sys.argv[1]))))

If you run this code with python fraction.py 2 you should have 4/15 but here's what I get:

4803839602528529/18014398509481984

which is numerically correct I think, when I just calculate it i get 0.26666666666666666 (maybe both fractions are different at x digits from 0).

What is the problem here?

Answer 1

Convert to Fraction objects before you do the math, not after:

def t(n):
    n = Fraction(n)
    if n==0:
        return n
    else:
        return 1/(4-t(n-1))

If you do the math before converting to a Fraction , the math gets done as floating point math, giving you an imprecise result which then you convert to an imprecise Fraction .

If you convert first, then the math gets done as fraction math and things stay precise.