When implementing currency with integers, actually with fixed-point numbers, there is no difficulty in having an exchange rate with the same precision as the integer format, i.e. up to 18-19 digits for 64-bit integers.

You just have to implement the conversion function carefully, i.e. the exchange ratio would actually be represented not by a single number, but by a ratio of suitable integers, to ensure no loss of precision during the conversion done by exact multiplication with extended double-word result and then division.