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Reciprocal cycles

Problem 26

Published on 13 September 2002 at 06:00 pm [Server Time]

A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:

1/20.5
1/30.(3)
1/40.25
1/50.2
1/60.1(6)
1/70.(142857)
1/80.125
1/90.(1)
1/100.1

Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.

Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part.


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