How to convert incredibly long decimals to fractions and back with high precision

Question

I'm trying to convert very large integers to decimals, then convert those decimals to Fractions, and then convert the Fraction back to a decimal. I'm using the fractions and decimal packages to try and avoid floating point imprecision, however the accuracy still tapers off rather quickly. Is there any way to fix this / other ways of doing this?


import fractions
import decimal


def convert(exampleInt):
    power_of_10 = len(str(exampleInt))
    decimal.getcontext().prec = 10000
    exampleDecimal = decimal.Decimal(exampleInt) / (decimal.Decimal(10) ** power_of_10)
    exampleFraction = fractions.Fraction(str(exampleDecimal)).limit_denominator()
    backToDecimal = exampleFraction.numerator / decimal.Decimal(exampleFraction.denominator)
    print(f"backToDecimal: {backToDecimal}")


convert(34163457536856478543908582348965743529867234957893246783427568734742390675934285342)

Which outputs: .341634575369123189552597490138153768602695082851231192155069838....

Calling "limit_denominator" with its default argument reduces precision considerably. — Michael Butscher, Dec 28 '22 at 19:21
Why do they need to be `Fraction` objects? You already know what fraction they are—that’s how you’re forming the `Decimal` objects. — Davis Herring, Dec 28 '22 at 23:56

relent95 · Accepted Answer · 2023-01-07T10:41:09.633

4

It's because of calling the limit_denominator(). Also it's quite inefficient to convert using an intermediate string.

Convert a Decimal object into a Fraction object using the constructor like the following.(It's Mark Dickinson's solution.)

import fractions
import decimal

decimal.getcontext().prec = 100

d = decimal.Decimal(34163457536856478543908582348965743529867234957893246783427568734742390675934285342)
d = d / 10**(d.adjusted() + 1)

f = fractions.Fraction(d) # This is equivalent to Fraction(*d.as_integer_ratio())
d2 = decimal.Decimal(f.numerator) / f.denominator
assert(d2 == d)

edited Jan 07 '23 at 10:41

answered Dec 29 '22 at 01:46

relent95

3,703
1
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You shouldn't need `as_integer_ratio` here; just `fractions.Fraction(d)` should be enough to convert a `decimal.Decimal` instance `d` to a `fractions.Fraction` instance with the exact same value. – Mark Dickinson Jan 06 '23 at 19:21
1

Thanks @Mark Dickinson, I updated the answer. – relent95 Jan 07 '23 at 10:44

How to convert incredibly long decimals to fractions and back with high precision

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