Fractions with a repeating decimal of a specific period

2004Kenneth Levasseur
Mathematical Sciences
UMass Lowell

This page was motivated from work done by teachers at the Focus on Mathematics Summer Institute on Algebra during the week of August 9, 2004 and specifically by an observation by Paul Grady, from Waltham HS.  I'm not going to describe the way this works since it will spoil the opportunity you have to figure it out on your own!

At issue is whether, given a positive integer k, there exists an integer n such that the decimal represention of 1/nhas period k.   For example, if k = 5, we can point to FormBox[RowBox[{1/41, =, FormBox[RowBox[{0.024390243902439024390, …}], TraditionalForm]}], TraditionalForm]

Estimated maximum input is about 30-35. "Time-out" will result from larger inputs.

Enter the period you desire and an attempt will be made to
find a fraction that has a repeating decimal representation
with that period.

Estimated maximum input is about 30-35

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