\[0.111\dots \quad \div \quad 0.222\dots \quad \times \quad 0.333\dots \quad \div \quad 0.444\dots \quad \times \quad 0.555\dots \quad \div \quad 0.666\dots \quad \times \quad 0.777\dots \quad \div \quad 0.888\dots \quad \times \quad 0.999 \]

Compute the number above and round your answer to 3 decimal places.

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