Question

What I need to do is use integer arithmetic to convert fractions into floating point numbers. The number of decimal places needed is specified as a variable DECIMALS. Each fraction is contained in a tuple of integers, for example (1, 3). The first item is the numerator and the second is the denominator. The tuples are contained in a list called fractions.

This is my code so far:

fractions = [(1,7), (2,3), (22,7), (7001,7), (9,3), (611951,611953), (1,11), (1,7689585)]

DECIMALS = 10**40 # 40 decimal places

for fraction in fractions:  
     x =  DECIMALS*fraction[0]/fraction[1]
     print x

When i run the code this is what i get:

1428571428571428571428571428571428571428
6666666666666666666666666666666666666666
31428571428571428571428571428571428571428   
10001428571428571428571428571428571428571428
30000000000000000000000000000000000000000
9999967317751526669531810449495304377950
909090909090909090909090909090909090909
1300460297922449651053990559958697

The problem is that I need to format this into the correct decimal format. What I tried was

print "0.%.40d" % (x)

But of course this will only help me with the first 2 decimals; the rest will be wrong. I thought about dividing it up so I can calculate the fractions indivdually to make them easier to format, but I have no idea how to do this. The catch is that all the fractions need to be processed by the same code. I also want it to be rounded properly but thats not a big deal right now.

Answer 1

If it strictly formatting, as implied by your question, you could, of course, do this with integers and strings alone:

def intF(n, d, l=40):
    s=str(n*10**l / d)
    if len(s) < l:
        return '0.{:0>{width}}'.format(s,width=l)
    if len(s) > l:
        return s[0:len(s)-l]+'.'+s[len(s)-l:] 

    return '0.'+s


for f in [(1,7), (2,3), (22,7), (7001,7), (9,3), 
          (611951,611953), (1,11),(1,7689585)]:
    print intF(*f)
    print float(f[0]) / f[1]
    print 

Output:

0.1428571428571428571428571428571428571428
0.142857142857

0.6666666666666666666666666666666666666666
0.666666666667

3.1428571428571428571428571428571428571428
3.14285714286

1000.1428571428571428571428571428571428571428
1000.14285714

3.0000000000000000000000000000000000000000
3.0

0.9999967317751526669531810449495304377950
0.999996731775

0.0909090909090909090909090909090909090909
0.0909090909091

0.0000001300460297922449651053990559958697
1.30046029792e-07

The last digit will not correctly round and it will not handle edge cases (‘inf’, ‘NaN’, division by zero, etc) correctly.

Works in a pinch I suppose.

Why not use the batteries included though, like Decimal or Fraction?