When would get an answer with three decimal places?

Answer 1

Lots of calculations use 3 decimal places. A common example that you encounter often (but probably rarely think about it) is when you buy gasoline. The big sign may say 3.01 per gallon, but notice that little 9 after it. The actual price is $3.019

This doesn't exactly answer your question, since you want when the answer is 3 decimals, and the gas pumps always round to the nearest cent (2 decimals).

If you convert some fractions to a decimal, you can get 3 or more decimals as an answer: 3/8 = 0.375, for example.

Sales tax calculations can result in 3 or more decimal places (which are usually carried through to the final result, before rounding to 2 decimal places).