Express the recurring decimal $0.\overline{36}$ (that is, $0.363636\ldots$) as a fraction in its lowest terms.
A$\dfrac{9}{25}$
B$\dfrac{1}{3}$
C$\dfrac{4}{11}$CORRECT
D$\dfrac{36}{100}$
JUPEBMathematicsSequences and Series
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Why the answer is C, and why the others tempt you.
The decimal is the geometric series $0.36 + 0.0036 + 0.000036 + \ldots$ with first term $0.36$ and ratio $0.01$, so its sum is $\dfrac{0.36}{1 - 0.01} = \dfrac{0.36}{0.99} = \dfrac{36}{99} = \dfrac{4}{11}$. The fraction $\dfrac{9}{25}$ equals $0.36$ exactly, without the recurrence.
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