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In the year 1796, the first U.S. dimes were produced for circulation. Thus, I think it would be reasonable to say that the origins of this phrase came sometime after, right? From what I can tell, it looks like this phrase originated in the 1800s where various foods were being sold by the dozen for the price of a dime. Several newspapers from that time, for instance, were advertising how things like eggs, oranges, or peaches, were available by the dozen, and their cost was nothing more than a single dime. An example of this comes from the Galveston Daily News, 1866:

    "The San Antonio Ledger says the city is well stocked with peaches at a dime a dozen."

The earliest quote that I could find of this idiom being used with its figurative meaning of 'something that's very common and/or considered to be of small worth' is from The Northern Miner newspaper, 1931:

    "'Carners,' the old-timer said, 'is just an overgrown clown. As for the others--Schaof, Baer, 
      Paulino, Risko, Campolo--they're nothing but 'dime a dozen fighters.' "

Another example of this expression being used in a figurative sense comes from the Sandusky Register, 1937: 

    "Smiles were a dime a dozen in the Yankee clubhouse. Even Colonel Ruppert, owner of the
     club, was so stated he went from player to player shaking hands."
* Hugs were a dime a dozen at our family reunion since everyone was so happy to see one another.
Note: There are times when the origins of a saying are not clear. In such cases, what I'll usually do is list some of the more plausible theories that exist about how or where the phrase may have come from. Take these, for the most part, with a grain of salt.

Additionally, I typically try to find the oldest quotes I can that contain the expression. Keep in mind, however, that it's possible even older quotes exist and I just don't know about them.
The meaning for a Dime a Dozen.

The phrase 'a dime a dozen' is used to describe things that are abundant in quantity and/or very cheap; something that's easily acquired.
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