Is money discrete or continuous data?

Answer 1

Both.

When we use money for purchases, it is in discrete units, so many dollars and cents.

When we use money in calculations, it is a continuous value, and we have to use rounding to get discrete values.

Example: I go to the store and buy a bag of coffee for $5.40. I must give the person 5 dollars and 40 cents. This is a discrete value.

But if there's sales tax, let say 7%, this tax comes to $0.378 so we round up to $0.38 as the tax that is due.