In the U.S. is a dime is a ten cent coin?

Answer 1

Yes. A dime is a 10c coin. A 5c coin is called a nickel and 25c a quarter.

History of the names:

Dime:

The word "dime" comes from the obsolete word "disme", which is itself derived from the French word "dixième" ("deez-YEM") meaning "one tenth". When the U.S. coinage system was first developed it was intended to be based on multiples of 10 rather than 100. Denominations were:

Mill (or mil) - 1/1000 of a dollar
Cent - 1/100
Dime - 1/10
Dollar
Eagle - 10 dollars
Union - 100 dollars

The mill proved too small and the union too large for practical use so these denominations were never issued.

Prices were expected to be expressed using a variation on the old British style; something like 1/3/5 or 1.3.5 would mean "1 dollar, 3 dimes, and 5 cents". That proved cumbersome so from almost the start, most prices were expressed using just dollars and cents along with the $ sign; e.g. $1.35. However the 10¢ coin had achieved a life of its own as a "dime" and the name has stuck for over 200 years.

Nickel:

The nickel wasn't part of the first coinage system. Each denomination was also divided into halves, so there were half-eagles, half-dollars, half-dimes, and half-cents. The half-dime was a very tiny coin that became increasingly impractical in daily commerce. By the mid-1860s coin manufacture had improved to the point where nickel, a very hard metal, could be used to make coins that lasted longer than traditional silver ones. Two new copper-nickel coins were introduced - a 3¢ coin designed for purchasing postage stamps, and a new, larger 5¢ coin to replace the half-dime. To distinguish them they were called "3 cents, nickel" and "5 cents, nickel", or sometimes "3-cent nickels", etc. The 3-cent coin was eventually discontinued so the name "5-cent nickel" was shortened to just "nickel". Interestingly enough, the coin is mostly copper!

Quarter:

The 25¢ piece remains the oddball in an otherwise 10-based coinage system. In true decimal systems such as those used in the UK, EU, Australia, NZ, etc. all denominations are based on factors and multiples of 10 so the corresponding coin is 20 cents, not 25. The U.S. is different because at the time of independence, large parts of the country were using large Spanish coins as the primary currency unit. They were about the size that would be used for silver dollars and were in fact known as "Spanish milled dollars". There were no smaller coins and the practice was to make change by cut the soft silver coins into halves, quarters, and eighths like Pizza slices (You can look it up!!). The Spanish milled dollar remained legal tender after the US started minting its own coins, so a quarter-dollar coin was made in order to be compatible with the slices. Spanish milled dollars were demonetized in 1857 but by that point the quarter had become such an integral part of the US system that attempts to replace it with a 20¢ piece have failed.

As a side note, a 1/8 slice of a Spanish dollar was called a "bit", which is the source of the slang expression "2 bits" for a quarter!