Getting lots of digits of constants

constants.hs

import Prelude hiding (pi)

import Data.Ratio ((%))

import Data.List(findIndex, splitAt)
-- Thanks to augustss on stackoverflow
showRational :: Int -> Rational -> String
showRational n r =
    let d = round (abs r * 10^n)
        s = show (d :: Integer)
        s' = replicate (n - length s + 1) '0' ++ s
        (h, f) = splitAt (length s' - n) s'
    in  (if r < 0 then "-" else "") ++ h ++ "." ++ f

approx = showRational 1000

pi :: Rational
pi = 2 *  pi' 5000 1 3 

pi' :: Integer -> Integer -> Integer -> Rational
pi' 0 _ _ = 0
pi' n a b = 1 + (a % b) * (pi' (n-1) (a+1) (b+2))

fac n = product [1..n]

e :: Rational 
e = sum [1 % fac n | n <- [0..1000]]

main = print (approx pi) >> print (approx e)