express the numbers in form of p/q
15.71212121212121212121212121212121212121212121212121212121212121212121212121212121212121211212121212121212121212121212121212121212121212121212121212...................................................................................
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So 15.712(bar on 12) in the form of p/q where p and q are integers and q is not equal to 0 is 15015/990. This can further be simplified to 5005/330 = 1001/66. Therefore the final answer is 15.712(bar on 12) = 1001/66.
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