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    <p>To find the repeating pattern, just keep track of the values you use along the line:</p> <pre><code>1/5 = 1/101: 1 &lt; 101 =&gt; 0 (decimal separator here) 10 &lt; 101 =&gt; 0 100 &lt; 101 =&gt; 0 1000 &gt;= 101 =&gt; 1 1000 - 101 = 11 110 &gt;= 101 =&gt; 1 110 - 101 = 1 10 -&gt; match </code></pre> <p>As you reach the same value as you had at the second bit, the process will just repeat from that point producing the same bit pattern over and over. You have the pattern "0011" repeating from the second bit (first after decimal separator).</p> <p>If you want the pattern to start with a "1", you can just rotate it until it matches that condition:</p> <pre><code>"0011" from the second bit "0110" from the third bit "1100" from the fourth bit </code></pre> <p>Edit:<br> Example in C#:</p> <pre><code>void FindPattern(int n1, int n2) { int digit = -1; while (n1 &gt;= n2) { n2 &lt;&lt;= 1; digit++; } Dictionary&lt;int, int&gt; states = new Dictionary&lt;int, int&gt;(); bool found = false; while (n1 &gt; 0 || digit &gt;= 0) { if (digit == -1) Console.Write('.'); n1 &lt;&lt;= 1; if (states.ContainsKey(n1)) { Console.WriteLine(digit &gt;= 0 ? new String('0', digit + 1) : String.Empty); Console.WriteLine("Repeat from digit {0} length {1}.", states[n1], states[n1] - digit); found = true; break; } states.Add(n1, digit); if (n1 &lt; n2) { Console.Write('0'); } else { Console.Write('1'); n1 -= n2; } digit--; } if (!found) { Console.WriteLine(); Console.WriteLine("No repeat."); } } </code></pre> <p>Called with your examples it outputs:</p> <pre><code>.1 No repeat. .01 Repeat from digit -1 length 2. .10 Repeat from digit -1 length 2. 1.0 Repeat from digit 0 length 2. .0011 Repeat from digit -1 length 4. </code></pre>
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    1. POAlgorithm for detecting repeating decimals?
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    1. POAlgorithm for detecting repeating decimals?
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    1. COim not sure if this solves his problem because some fractions repeat after a certain number of digits for example 5/6 = .8333333. so under your model it would use the 8 to find a repetition.
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    2. CO@letseatunch: 5/6 = 101/110 = 0.11010101010101010... If you run FindPattern(5,6) it will find the pattern repeating from digit -2 with the length 2.
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    3. COIt took me a little while to understand your code because I don't know C# very well, but I think this is exactly for what I was looking. I'm writing this in C++ and the number storage isn't exactly that way, but it should be easy enough to port this over. Thank you very much for your help!
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