While a coins with a denomination of three cents may seem rather odd today, a century and a half or so ago it made considerably more sense. For one thing, the price of a postage stamp was three cents, so rather than require three cumbersome large cents (through 1857) it was felt that a simple three cent coin could facilitate their purchase. Secondly, with the hoarding of silver coins during the Civil war and the resulting disappearance of small change, two new coins of three and five cents struck in nickel and a two-cent piece in bronze appeared between 1864-66 to ease the shortage.
What is most important to keep in mind however, was the purchasing power difference between then and now. Three cents during the 1850s and 1860s would equate to between 50 and 75 cents today – not an insignificant sum. So the utility of coins denominated between one and five cents takes on a whole new meaning when viewed in this context.
By the 1870s and 1880s, the bronze cent and the five-cent nickel coin had established themselves in the channels of commerce, and both the two cent and three cent denominations were seen as unnecessary. The Coinage Act of 1873 eliminated the two-cent piece, the three-cent piece in silver and the silver half dime. The three-cent piece in nickel survived until 1889, though mintage quantities after 1875 were usually very low – 1881 being the only “common” date.