## Overview

### Question

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

\begin{aligned} \frac{1}{2}&=0.5 \\\\ \frac{1}{3}&=0.\overline{3} \\\\ \frac{1}{4}&=0.25 \\\\ \frac{1}{5}&=0.2 \\\\ \frac{1}{6}&=0.1\overline{6} \\\\ \frac{1}{7}&=0.\overline{142857} \\\\ \frac{1}{8}&=0.125 \\\\ \frac{1}{9}&=0.\overline{1} \\\\ \frac{1}{10}&=0.1 \end{aligned}

Where $$0.1\overline{6}$$ means $$0.1666\dots$$, 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.

983