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Recurring decimal as a fraction

Authors
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    Name
    Vu Hung
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Problem Statement

Express 0.230.\overline{23} as a rational number.


Solutions

0.23=2399.0.\overline{23}=\frac{23}{99}.

A geometric view is

0.23+0.0023+0.000023+0.23+0.0023+0.000023+\cdots

with first term 23100\frac{23}{100} and ratio 1100\frac{1}{100}.


Further Readings


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