The type system in SQLite is not as strict as it is in other RDBMS.
If you don’t need irrational numbers (few financial applications do?), the tuple of (value, scale) can take you very far.
Floating point (up to a certain amount of absurdity) you can describe with integers (value, scale).
Real numbers you can describe with integers (numerator, denominator, scale).
Irrationals are more difficult. That's why we try not to use them :). Hopefully your company's commission tiers are not defined in terms of circles or euclidean distances.
Sure you can round at the end but then you have to worry about compounding errors.
I know how to do it, it is just not practical.
Strings does not overflow & are easy to transfer.
Unless you operate 2+degree currency polynomials, it may be okay to store money in minimal integer units at an application level too. It may be adjusted in only ui formatters. One should be careful with constants in code and external apis, but nothing you can’t get used to or catch with a test. We store timeouts in milliseconds, weights in grams, and so on anyway - not a new thing.
As an example, the primary database I maintain for our company is able to hold decimal .00 natively, but we use its fields as if they were multiplied by 1000, i.e. 12,345.00 is stored and operated as 12.35 (and goes as int64 1235 to ODS) (rounding 5.00 off is fine for this particular accounting model). Nobody made a three-digit mistake ever in a whole decade, because square/cubic money is not a thing naturally, and ratios & exchange rates work as usual. It is like storing cents, but the other way round.
Storing in-app amounts in floats has a downside of accumulating an error in for-looped calculations and the need for periodic rounding (although it should run on a really big dataset to collect that enough). If a language has a money type and it can be programmed accordingly, then a problem disappears. If not, then it persists either way in different forms.
I mean I know there are min/max ranges in the float specification that can guarantee no loss of accuracy to two decimal places... but then I need to manually make sure there's never anywhere in the code that might ever sum up transactions to beyond that, or whatever. Or people thinking it's OK to divide and then multiply, which you're hopefully less likely to do if it's an integer.
I feel much more peace of mind storing currency data as integers and doing the conversion. It feels quite natural really, since I'm already used to doing that with datetimes for different timezones.
You so not want to invent your own arbitrary precision numbers