Reciprocal cycles

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

\[ \begin{align} \frac{1}{2}\ &=0.5\\ \frac{1}{3}\ &=0.(3)\\ \frac{1}{4}\ &=0.25\\ \frac{1}{5}\ &=0.2\\ \frac{1}{6}\ &=0.1(6)\\ \frac{1}{7}\ &=0.(142857)\\ \frac{1}{8}\ &=0.125\\ \frac{1}{9}\ &=0.(1)\\ \frac{1}{10}&=0.1 \end{align} \]

Where \( 0 \).\( 1 \)(\( 6 \)) means \( 0 \).\( 166666... \), and has a \( 1 \)-digit recurring cycle. It can be seen that \( \frac{1}{7} \) has a \( 6 \)-digit recurring cycle.

Find the value of \( d \) \( <1000 \) for which \( \frac{1}{d} \) contains the longest recurring cycle in its decimal fraction part.