Exactly. Then you realize you need to deal with values with different scales, because "amount of money" may need 2 decimal places while "exchange rate" may need

Exactly. Then you realize you need to deal with values with different scales, because "amount of money" may need 2 decimal places while "exchange rate" may need 3, so you start tracking scales. At which point you've just reinvented basically the same data type as described here.