Using arbitrary precision doesn't make sense if the data needs to be stored in a database (for most situations at least). Regardless, infinite precision is magical thinking anyway: try adding Pi to your bank account without loss of precision.
Fixed point is a general technique that is commonly done with machine integers when the necessary precision is known at compile time. It is frequently used on embedded devices that don't have a floating point unit to avoid slow software based floating point implementations. Limiting the precision to $0.01 makes sense if you only do addition or subtraction. Precision of $0.001 (Tenths of a cent also called mils) may be necessary when calculating taxes or applying other percentages although this is typically called out in the relevant laws or regulations.