Well, not really.

Today's dollar came into being in 1971 (fully off gold denomination). That dollar existed only since 1965 (end of silver coinage). That dollar in turn existed only since 1945 (Bretton Woods agreement). That dollar came into being in 1934 (confiscation of personal gold), and that dollar was in turn birthed in 1913 (Federal Reserve Act came into effect). The previous dollar was the initial one.

So I guess that makes today's dollar Dollar 6.0.

You might be able to argue a case for some of these steps being n.1 instead of (n+1).0, but today's dollar certainly has zero resemblance to the dollar of the late 18th century.