The Number One Dime is the first coin that Scrooge McDuck ever earned (or, according to some stories, produced). It first appeared in the story titled "The Round Money Bin", created by Carl Barks and first published in Uncle Scrooge #3 (September, 1953). In this story, the dime is so old that it has become thin as a razor blade and allows Scrooge to cut binding ropes and escape from the Beagle Boys.
The number one dime is a 10¢ silver 1875 Seated Liberty Dime. It is usually seen encased in a reliquary shaped like a golden platter with a velvet cushion securing the coin under a protective glass dome. In DuckTales, the cushion is replaced by a dollar sign-shaped pedestal.
In later stories, it is insinuated that the dime brings good luck to Scrooge and has helped him become a rich man, and in some stories he instantly starts losing money whenever the dime is no longer in his possession. It is never made clear whether the dime actually brings good luck or if Scrooge merely believes in it so much that he is distressed and makes bad decisions whenever he no longer has the dime. Since Barks never actually said that it was because of the coin that Scrooge was the richest duck in the world, Don Rosa, after various information exchanges with Barks, for a faithful production of The Life and Times of Scrooge McDuck, clarified that the Number One Dime is not actually an amulet, and that this vision was just a myth. The Number One Dime is just a sentimental object that happens to be the first coin Scrooge received for his work. Rosa made clear, also, that Scrooge made his fortune working hard and being honest. This point is heavily reinforced in DuckTales where Scrooge basically tells his nephews about the value of hard earned cash.
The dime is a key plot point in practically every story featuring Magica De Spell as the main villain. Magica believes that by stealing the first coin earned by the richest person in the world and melting it down to a magical amulet, she can gain the power of the ancient King Midas, so that everything she touches becomes gold and she can be rich beyond her wildest dreams. The fact that this will only work if the coin indeed belongs to the richest person in the world at the time, and is the first coin that person earned, is crucial, and is made into a plot point in some stories.
According to a comic story by Don Rosa, it is an 1875 Seated Liberty dime, but in a comic story written by Pat and Carol McGreal and drawn by Maximino Tortajada Aguilar, the last two digits have been swapped, making it an 1857 Seated Liberty dime.
Scrooge earned the dime in 1877 in his hometown of Glasgow, when he started working as a shoeshine boy on his tenth birthday. Before that it belonged to Howard Rockerduck (the father of John D. Rockerduck). The customer who paid it to him, a ditch-digger called Burt, "cheated" Scrooge, as an American dime would be worthless in Scotland (Seated Liberty dimes were discontinued in 1891). In reality, Scrooge's father, Fergus McDuck, gave Burt the dime specifically for paying Scrooge for his services. Scrooge McDuck never learned that fact, although Fergus did reveal it to Scrooge's sisters Matilda and Hortense. Burt and Magica De Spell, who learned about this when she traveled in time to the day Scrooge earned the Dime, are the only other ones who know. Scrooge kept it as a reminder not to be fooled again in the future. When he emigrated to the US three years later, he carried it with him. Scrooge still has the dime and keeps it on a pillow under glass because it is very special to him. Donald Duck, Huey, Dewey, and Louie, and Gladstone Ganderamong many others think it is really a lucky charm, but Scrooge himself maintains it has only sentimental value.