How to know the repeating decimal in a fraction?

Question

I already know when a fraction is repeating decimals. Here is the function.

public bool IsRepeatingDecimal
{
    get
    {
        if (Numerator % Denominato         


        

Answer 1

I came here expecting to be able to copy & paste the code to do this, but it didn't exist. So after reading @Patrick87's answer, I went ahead and coded it up. I spent some time testing it thoroughly and giving things a nice name. I thought I would leave it here so others don't have to waste their time.

Features: If the decimal terminates, it handles that. It calculates the period and puts that in a separate variable called period, in case you want to know the length of the reptend.

Limitations: It will fail if the transient + reptend is longer than can be represented by a System.Decimal.

public static string FormatDecimalExpansion(RationalNumber value)
{
    RationalNumber currentValue = value;

    string decimalString = value.ToDecimal().ToString();
    int currentIndex = decimalString.IndexOf('.');

    Dictionary dict = new Dictionary();
    while (!dict.ContainsKey(currentValue))
    {
        dict.Add(currentValue, currentIndex);

        int rem = currentValue.Numerator % currentValue.Denominator;
        int carry = rem * 10;

        if (rem == 0) // Terminating decimal
        {
            return decimalString;
        }

        currentValue = new RationalNumber(carry, currentValue.Denominator);
        currentIndex++;
    }

    int startIndex = dict[currentValue];
    int endIndex = currentIndex;
    int period = (endIndex - startIndex); // The period is the length of the reptend

    if (endIndex >= decimalString.Length)
    {
        throw new ArgumentOutOfRangeException(nameof(value),
            "The value supplied has a decimal expansion that is longer" +
            $" than can be represented by value of type {nameof(System.Decimal)}.");
    }

    string transient = decimalString.Substring(0, startIndex);
    string reptend = decimalString.Substring(startIndex, period);

    return transient + $"({reptend})";
}

And for good measure, I will include my RationalNumber class. Note: It inherits from IEquatable so that it works correctly with the dictionary:

public struct RationalNumber : IEquatable
{
    public int Numerator;
    public int Denominator;

    public RationalNumber(int numerator, int denominator)
    {
        Numerator = numerator;
        Denominator = denominator;
    }

    public decimal ToDecimal()
    {
        return Decimal.Divide(Numerator, Denominator);
    }

    public bool Equals(RationalNumber other)
    {
        return (Numerator == other.Numerator && Denominator == other.Denominator);
    }

    public override int GetHashCode()
    {
        return new Tuple(Numerator, Denominator).GetHashCode();
    }

    public override string ToString()
    {
        return $"{Numerator}/{Denominator}";
    }
}

Enjoy!