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Fraction of a recurring decimal

Authors
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    Name
    Vu Hung
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Problem Statement

Find the fraction for 0.1˙2˙3˙0.\dot{1}\dot{2}\dot{3}?

Hints

Use a=1231000a = \frac{123}{1000} and r=11000r = \frac{1}{1000} in your S∞S_\infty formula.

Solutions

S∞=12310001−11000=123999=41333.S_\infty = \frac{\frac{123}{1000}}{1 - \frac{1}{1000}} = \frac{123}{999} = \frac{41}{333}.

Takeaways

  • Every recurring decimal is a geometric series sum S∞S_\infty.

Further Readings

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