Convert Ratio To Decimal
May 15, 2015
Here’s our solution, which was indeed written within fifteen minutes:
(define (decimal num denom digits)
(let loop ((num (* (modulo num denom) 10))
(out (cons #\. (reverse (string->list
(number->string (quotient num denom))))))
(digits digits))
(if (zero? digits)
(list->string (reverse out))
(loop (* (modulo num denom) 10)
(cons (integer->char (+ (quotient num denom) 48)) out)
(- digits 1)))))
This is nothing more than the grade-school long-division algorithm, generating the output one digit at a time; out is initialized to the part of the quotient to the left of the decimal point, in reverse:
> (decimal 3227 557 30)
"5.793536804308797127468581687612"
You can run the program at http://ideone.com/hiNpKQ.
Programming Praxis 
In Python.
from decimal import Decimal, getcontext def round_frac1(num, den, digits): getcontext().prec = digits return Decimal(num) / Decimal(den) def round_frac2(num, den, digits): res = ["" if num >= 0 else "-"] div, mod = divmod(abs(num), den) res += [str(div), "."] for d in range(digits): if mod == 0: break div, mod = divmod(mod * 10, den) res.append(str(div)) return "".join(res) print(round_frac1(3227, 557, 31)) # 5.793536804308797127468581687612 print(round_frac2(3227, 557, 30)) # 5.793536804308797127468581687612A quick ‘n dirty Haskell version.
-- The result of a/b with n digits after the decimal point. divide n a b = let (q, r) = a `quotRem` b in show q ++ "." ++ concatMap show (take n (r `fr` b)) where a `fr` b = let (q, r) = (10*a) `quotRem` b in q : (r `fr` b)A couple of examples in ghci:
In C++
#include
using namespace std;
int main()
{
int den,num,dig,temp1,temp2;
cout <> den;
cout <> num;
cout <> dig;
cout << num/den << "."; // Whole number part of decimal followed by decimal point
temp1=num;
for (int i=0;i<30;i++)
{
temp2=(temp1%den)*10;
cout << temp2/den;
temp1=temp2%den;
}
return 0;
}
In C++
Clojure
I admit, it took me longer than 15 minutes..
(defn long-division [nom denom decimals] (loop [result (str (quot nom denom) ".") nom (* (mod nom denom) 10) decimals decimals] (if (> decimals 0 ) (recur (str result (quot nom denom)) (* (mod nom denom) 10) (dec decimals)) result))) (println (long-division 3227 557 30))