Columnar Multiplication?

\[ \large{\begin{array}{cccccc} &0.& 1 & 6& 6 & 6&6& \ldots\\ \times&0. & 3 & 3& 3 & 3&3&\ldots\\ \hline &0. &0 &\bigstar &\bigstar& \bigstar& \bigstar&\ldots\\ \hline \end{array}} \]

The above shows the product of the two fractions \( \dfrac16 \) and \( \dfrac13 \) when written in decimal representation.

Find the value that represents the symbol \( \bigstar \).

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