The sign is first attested in British, American, Canadian, Mexican and other Spanish American business correspondence in the 1770s, referring to the Spanish American peso or "piece of eight" in British North America.
One theory says, the Spanish Peso provided the model for the currency that the United States later adopted in 1785.
Another theory says, this symbol was accepted by the US as around the same time the U.S. was minting its first dollar coins.
In 1792, Spanish currency was extensively circulated in the U.S. and around the world.
In large part due to this, the U.S. chose to design the U.S. dollar coins to duplicate the Spanish coins, in terms of matching the material and weight, hence value (at the time, the coins were made of silver and valued after the price of silver).
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