Перевести простую пробь в десятичную

#include <cstdlib>
#include <algorithm>
#include <iostream>
#include <iterator>
#include <sstream>
 
class RepeatingDecimal
{
public:
    typedef unsigned number_type;
    RepeatingDecimal(number_type numerator, number_type denominator);
    friend std::ostream& operator<<(std::ostream& out, const RepeatingDecimal& repeatingDecimal);
private:
    std::string resultAsString;
};
 
RepeatingDecimal::RepeatingDecimal(number_type numerator, number_type denominator)
{
    std::ostringstream sout;
    sout.exceptions(std::ostringstream::badbit | std::ostringstream::failbit);
    sout << numerator / denominator;
    numerator %= denominator;
    if (numerator != 0)
    {
        sout << '.';
        std::vector<number_type> digits, remainders{numerator};
        while (true)
        {
            numerator *= 10;
            digits.push_back(numerator / denominator);
            numerator %= denominator;
            auto repetitionStartRem =
                std::find(remainders.begin(), remainders.end(), numerator);
            if (repetitionStartRem != remainders.end())
            {
                auto repetitionStart =
                    digits.begin() + (repetitionStartRem - remainders.begin());
                std::copy(
                    digits.begin(), repetitionStart,
                    std::ostream_iterator<number_type>(sout)
                    );
                sout << '(';
                std::copy(
                    repetitionStart, digits.end(),
                    std::ostream_iterator<number_type>(sout)
                    );
                sout << ')';
                break;
            }
            remainders.push_back(numerator);
        }
    }
    resultAsString = sout.str();
}
 
std::ostream& operator<<(std::ostream& out, const RepeatingDecimal& repeatingDecimal)
{
    return out << repeatingDecimal.resultAsString;
}
 
int main(int argc, char* argv[])
{
    using namespace std;
 
    if (argc < 3)
    {
        cerr << "Error: too few arguments" << endl;
        return 1;
    }
 
    istringstream argin;
    unsigned numerator, denominator;
    argin.str(argv[1]);
    argin >> numerator;
    if (!argin || argin.peek() != istringstream::traits_type::eof())
    {
        cerr << "Error: invalid argument: " << argv[1] << endl;
        return 1;
    }
    argin.clear();
    argin.str(argv[2]);
    argin >> denominator;
    if (!argin || argin.peek() != istringstream::traits_type::eof())
    {
        cerr << "Error: invalid argument: " << argv[2] << endl;
        return 1;
    }
    cout << RepeatingDecimal(numerator, denominator);
    return 0;
}