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Express the repeating base-10 decimal number $ 0.0123456790123456790... $ as a fraction $ \dfrac{1}{x} $ in any base system up to hexadecimal such that $ x $ has a minimal number of only 0s and 1s.

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The fraction is

$\frac{1}{81}$

Which can be expressed

in base $9$ as $\frac{1}{100}$

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  • $\begingroup$ Not bad. It's optimal if I'm not mistaken. $\endgroup$ – Arnaud Mortier Apr 30 at 22:37

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