I have to show that the set defined by {x element of (0,1) : the decimal expansion of x has only odd digits} is uncountable.

My attempt: I suppose we can show this by contradiction, but I'm sure how to go about doing so. If we were to use Cantor's diagonal argument doesn't that rely on infinite decimal expansion, doesn't the fact we are only looking at expansions that have odd digits imply finite decimal expansion?