The American word dime equaling 10 cents or 1/10th of a dollar comes from..........
Latin roots. Decima meaning10th part.
It also has French influence.....disme (modern French, dime) meaning the church tithe of 10%.
And "dime" isn't a nickname for a 10¢ coin, like "nickel" is for a 5¢ coin.
Dimes actually have "one dime" written on them, not 10¢.
Dime is officially a subunit of the dollar, like a shilling was of the pound. But because the currency is decimal no one would ever say "3 dimes and 6 cents", (like we would have said "3 shillings and sixpence ") they'd just say 36 cents.
So dime effectively just became the name of the 10¢ coin.
Nickels have "five cents" on them. Nickels are so called because they replaced an equal valued silver half dime, which was also worth 5¢