"Is the smallest of U.S. Coin of small value?" I am not sure what you are asking? smallest size? smallest of value? small value?
I think you may be asking if these silver three cents were the smallest in physical size. I'm not entirely sure but I believe there may be some fractional gold that may be smaller in diameter.
What I am asking is if this 1853 III Cent coin, which is the smallest of U.S. Silver coins, is worth more than 3 cents.
At the time it was minted it was worth three cents. Today, yes it is worth substantially more.... Maybe $50.00 or so.
They are also smaller than a modern dime. diameter = 14mm a modern Roosevelt dime is 17.9mm Seated Liberty half dimes are 15.5mm whereas Liberty Head Gold Dollars were 13mm
