Can You Spot The Pattern?

$\large{\begin{array}{cccccccccc} &0.& 1 & 1& 1 & 1&1&1& 1&1&1& \ldots\\ \times&0. & 1 & 1& 1 & 1&1&1&1& 1&1&\ldots\\ \hline &0. &0 &1 &2& 3& 4&5&6&7&\diamondsuit&\ldots\\ \hline \end{array}}$

The above shows the product of the two fractions $\dfrac19$ and $\dfrac19$ when written in decimal representation.

Find the value that represents the symbol $\diamondsuit$ .