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Let X denote the figure which does not recur and assume they are l in number. Let Y denote recurring period of consisting of m figures. Let R denote the value of the recurring decimal. Then, R=0.XYYY Therefore, 10lR=X.YYY --- 1 And, 10l+m.R=XY.YY --- 2 Subtracting 1 from 2 we get, R=(XY-X)/(10l+m - 10l).
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