from string import index

n,d=1,7
def f(n, d):
    x = n * 9
    z = x
    k = 1
    while z % d:
        z = z * 10 + x
        k += 1
    return k, z / d

#print f(n,d)

# (.051,2) = .0515151... = 51/990
# n = len(s[index(s,'~'):])
def r(r, n):
    s = str(r)
    a,b = s[index(s,'.')+1:-n], s[-n:]
    al,l = len(a), len(a+b)
    u,v = 10**al, 10**l
    n,d = int(r*u-int(a if a<>''else 1)), v-u
    g = gcd(n,d)
    while g <> 1:
        n,d = n/g,d/g
        g = gcd(n,d)
    return (n,d)

gcd=lambda a,b:a if b==0 else gcd(b,a%b)
    
# These aren't all correct, but why?
print r(1.1,1) # = 10/9
print r(2.5,1) # = 23/9 		X
print r(0.4,1) # = 4/9			X
print r(0.142857,6) # = 1/7		X