On Tue, Aug 21, 2018 at 03:27:46PM -0700, Roger Lea Scherer wrote:
> So I'm trying to divide fractions, technically I suppose integers.
Python has a library for doing maths with fractions. Unfortunately it is
considerably too complex to use as a learning example, but as a
practical library for use, it's great.
py> from fractions import Fraction
py> a = Fraction(7, 9)
py> a * 3
Fraction(7, 3)
py> a + 2
Fraction(25, 9)
py> a - Fraction(1, 9)
Fraction(2, 3)
> So, for
> instance, when the user inputs a 1 as the numerator and a 2 as the
> denominator to get the float 0.5, I want to put the 0.5 as the key in a
> dictionary
Be careful. Floats are quirky:
py> Fraction(1, 3)
Fraction(1, 3)
but converting from a float reveals something strange:
py> Fraction(1/3)
Fraction(6004799503160661, 18014398509481984)
The problem is that the float generated by 1/3 is *not* equal to the
mathematical fraction 1 over 3. Computer floats have only a finite
precision, in the case of Python 64 bits. Fractions which are repeating
in binary cannot be represented as an exact float.
So the mathematically precise number 1/3 looks like this is decimal:
0.33333333... # need an infinite number of 3s
and like this in binary (base two):
0.01010101... # need an infinite number of 01s
Since that would take an infinite amount of memory, it is impossible to
store 1/3 as a floating point number. The closest we get in Python is
0.01010101010101010101010101010101010101010101010101 (binary)
which is precisely and exactly equal to
6004799503160661/18014398509481984
rather than 1/3.
The bottom line is this: if you try working with floats in this way,
you're likely to get surprised from time to time. See here for more
detail:
https://docs.python.org/3/faq/design.html#why-are-floating-point-calculations-so-inaccurate
More to follow in a second response.
--
Steve
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