Yes, paper money will float until it becomes waterlogged.
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As long as it can displace a volume of water equal to its mass (ie its density is less than that of the water) it will float. Most paper will have a density less than that of water (or can be so folded) so will float.
maybe, try IT YOU self
From paper
Paper and very thin plastic.
the serial numbers on paper money are used as a tracking device and help prevent fake money from being made and passed off easily as the real thing