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The last place that you might have seen a nondecimal unit is on the stock exchanges. U.S. stock exchanges used eighths or sixteenths of dollars until converting to decimals between 2000 and 2001.
The conversion triggered a reaction in 2003 from Wall Street firms. They were having steep drops in profits from stock trading. A good deal of the loss was supposed to be a result of the change of stocks trading in dollars and cents instead of fractions. And supposedly investors benefited from the switch to decimal currency units.