Math CentralQuandaries & Queries


Question from Adriana, a student:


0.1234567891011.......Is this fraction periodic?

Hi Adriana,

Suppose it is periodic and the length of the period is n digits. In constructing the decimal fraction above by stringing together consecutive integers, eventually you get to the integer 10n+1, that is 1 followed by n+1 zeros. Hence the repeating part (the repetend) must be all zeros which it clearly is not.

I hope this helps,

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