Lua does not provide integers, too. From their mailing list I have learnt that the IEEE rules guarantee, that e.g. doubles have absolutely now problem representing 32bit integers. You write the same here. It seems to not be intuitive, but IEEE took care of it.
But I wonder why you write that for values in 1/100 one should multiply by 100! Wouldn't an IEEE double have no problems with values with two decimal points, too?
Or are there many problems with that, e.g. that $0.01 + $0.01 might already cause rounding errors which do not even out by the clever IEEE rules?
Of course 2^54 woudln't be the highest value where one shouldn't worry anymore, but something smaller.
1/5 in decimal is 0.00110011... repeating in binary, therefore not exactly representable, therefore it could lead to errors. Not big errors, but enough that smart people would prefer not to use it for money.
To give a concrete example, 19.99 can't be exactly represented in floating-point, and ends up being 19.989something. If you have a price of $19.99 that's represented in floating-point, and if you truncate rather than round as you pass it off for display, you'll end up displaying a price of $19.98. With enough manipulation, the error can accumulate to the extent that rounding the result won't save you either.
But I wonder why you write that for values in 1/100 one should multiply by 100! Wouldn't an IEEE double have no problems with values with two decimal points, too? Or are there many problems with that, e.g. that $0.01 + $0.01 might already cause rounding errors which do not even out by the clever IEEE rules?
Of course 2^54 woudln't be the highest value where one shouldn't worry anymore, but something smaller.