dime (n.) Look up dime at Dictionary.com
chosen 1786 as name for U.S. 10 cent coin, from dime "a tenth, tithe" (late 14c.), from Old French disme (Modern French dîme) "a tenth part," from Latin decima (pars) "tenth (part)," from decem "ten" (from PIE root *dekm- "ten").

The verb meaning "to inform" (on someone) is 1960s, from the then-cost of a pay phone call. A dime a dozen "almost worthless" first recorded 1930. Phrase stop on a dime attested by 1927 (a dime being the physically smallest unit of U.S. currency; turn on a dime is from 1913).