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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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  • $\begingroup$ I attempted to clarify what your question is. Check my edit note for more details $\endgroup$ – HTM Apr 30 '19 at 23:29
  • $\begingroup$ Isn't this a math question? $\endgroup$ – Tzu Li May 5 '19 at 0:55
  • $\begingroup$ @TzuLi Unless there's a clever or elegant solution with an "aha" moment. $\endgroup$ – Rand al'Thor May 5 '19 at 13:44
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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 '19 at 22:37

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