Problem 273. Recurring Cycle Length (Inspired by Project Euler Problem 26)

Preface: This problem is inspired by Project Euler Problem 26 and uses text from that question to explain what a recurring cycle is.

Description

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

1/2  = 	0.5
1/3  =	0.(3)
1/4  = 	0.25
1/5  = 	0.2
1/6  = 	0.1(6)
1/7  = 	0.(142857)
1/8  = 	0.125
1/9  = 	0.(1)
1/10 = 	0.1

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.

Create a function that can determine the length of the recurring cycle of 1/d given d.