Thanks Carl. That has one minor drawback. It pastes the expression in literally and not as a syntactic unit. Of course, the user could always type a set of parentheses before pasting but might often forget. If it was pasted after a 'z' in an existing Input Cell, the 'z' would only be associated with the first term in the expression. So I went to a box structure as follows.
expr = N[x/3 + 2 y/3]
PasteButton["1/3",
RawBoxes@StyleBox[RowBox[{"(", ToBoxes[expr], ")"}],
NumberMarks -> False]]
When this is pasted into an Input Cell that contains an initial 'z' we now obtain:
z (0.333333 x + 0.666667 y)
This maintains full machine precision in the notebook, but not in the posting. It is now also editable.