MediumMathematicsHigh School (11–12)Algebra › Sequences and SeriesNumericalA-Level IB

Write 0.136 = 0.1363636… as a fraction in its lowest terms.

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Write $0.1\overline{36} = 0.1363636\ldots$ as a fraction in its lowest terms.

Need a reminder? The key ideaShow

The sum of the first $n$ terms is $S_n = \dfrac{a(r^n - 1)}{r - 1}$ for $r \ne 1$ , and $na$ for $r = 1$ . When $|r| < 1$ , the sum to infinity is $S_\infty = \dfrac{a}{1 - r}$ . A recurring decimal is a GP with ratio $\tfrac{1}{10}$ , $\tfrac{1}{100}$ and so on.

The worked solution

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Write 0.136 = 0.1363636… as a fraction in its lowest terms.

The worked solution

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