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    <p>I found the same paper that Matt referenced, and I took a second and implemented it in Python. Maybe seeing the same idea in code will make it clearer. Granted, you requested an answer in C# and I'm giving it to you in Python, but it's a fairly trivial program, and I'm sure it would be easy to translate. The parameters are <code>num</code> (the decimal number you'd like to convert to a rational) and <code>epsilon</code> (the maximum allowed difference between <code>num</code> and the calculated rational). Some quick test runs find that it usually only takes two or three iterations to converge when <code>epsilon</code> is around 1e-4.</p> <pre><code>def dec2frac(num, epsilon, max_iter=20): d = [0, 1] + ([0] * max_iter) z = num n = 1 t = 1 while num and t &lt; max_iter and abs(n/d[t] - num) &gt; epsilon: t += 1 z = 1/(z - int(z)) d[t] = d[t-1] * int(z) + d[t-2] # int(x + 0.5) is equivalent to rounding x. n = int(num * d[t] + 0.5) return n, d[t] </code></pre> <p>Edit: I just noticed your note about wanting them to work with recurring decimals. I don't know any languages that have syntax to support recurring decimals, so I'm not sure how one would go about handling them, but running 0.6666666 and 0.166666 through this method return the correct results (2/3 and 1/6, respectively).</p> <p>Another Edit (I didn't think this would be so interesting!): If you want to know more about the theory behind this algorithm, <a href="http://en.wikipedia.org/wiki/Euclidean_algorithm" rel="noreferrer">Wikipedia has an excellent page on the Euclidian algorithm</a></p>
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    1. POAlgorithm for simplifying decimal to fractions
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    1. COYou don't need an array, btw; I posted an answer somewhere on SO once expressing the same algorithm as a Python generator (which avoids the need for epsilon and max_iter in the core logic as well).
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    2. COAh, here: http://stackoverflow.com/questions/445113/approximate-greatest-common-divisor/479028#479028
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    3. COYeah, initially I just did with with d0 and d1, but was less readable so I went with the list instead. Also, max_iter and epsilon just get moved elsewhere if you take them out, and I think it would be more convenient for an API user to do the whole thing in a single function call, rather than require the caller to do the iteration themselves.
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