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The thickness of a sheet is reduced by rolling (without any change in width) using $600 \: mm$ diameter rolls. Neglect elastic deflection of the rolls and assume that the coefficient of friction at the roll-workpiece interface is $0.05$. The sheet enters the rotating rolls unaided. If the initial sheet thickness is $2 \: mm$, the minimum possible final thickness that can be produced by this process in a single pass is ______ $mm$ (round off to two decimal places).

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