如何知道分数中的循环小数？

我已经知道分数何时是重复小数。这是函数。

public bool IsRepeatingDecimal
{
    get
    {
        if (Numerator % Denominator == 0)
            return false;

        var primes = MathAlgorithms.Primes(Denominator);

        foreach (int n in primes)
        {
            if (n != 2 && n != 5)
                return true;
        }

        return false;
    }
}

现在，我正在尝试获取重复的数字。我正在检查这个网站：http://en.wikipedia.org/wiki/Repeating_decimal http://en.wikipedia.org/wiki/Repeating_decimal

public decimal RepeatingDecimal()
{
    if (!IsRepeatingDecimal) throw new InvalidOperationException("The fraction is not producing repeating decimals");

    int digitsToTake;
    switch (Denominator)
    {
        case 3:
        case 9: digitsToTake = 1; break;
        case 11: digitsToTake = 2; break;
        case 13: digitsToTake = 6; break;
        default: digitsToTake = Denominator - 1; break;
    }

    return MathExtensions.TruncateAt((decimal)Numerator / Denominator, digitsToTake);
}

但我真正意识到，有些数字的部分小数是有限的，后来是无限的。例如：1/28

您知道更好的方法吗？或者算法？

一个非常简单的算法是这样的：实现长除法。记录你所做的每一次中间划分。一旦你看到一个与你之前做过的相同的划分，你就知道了正在重复的事情。

示例：7/13。

1. 13 goes into   7 0 times with remainder  7; bring down a 0.
2. 13 goes into  70 5 times with remainder  5; bring down a 0.
3. 13 goes into  50 3 times with remainder 11; bring down a 0.
4. 13 goes into 110 8 times with remainder  6; bring down a 0.
5. 13 goes into  60 4 times with remainder  8; bring down a 0.
6. 13 goes into  80 6 times with remainder  2; bring down a 0.
7. 13 goes into  20 1 time  with remainder  7; bring down a 0.
8. We have already seen 13/70 on line 2; so lines 2-7 have the repeating part

该算法给我们 538461 作为重复部分。我的计算器显示 7/13 是 0.538461538。对我来说看起来不错！剩下的就是实现细节，或者找到更好的算法！