What causes floating point rounding errors

Lua claims that floating point numbers can represent integer numbers just as exactly as integer types can, and I'm inclined to agree. There's no imprecise representation of a fractional numeric part to deal with. Whether you store an integer in an integer type, or store it in the mantissa of a floating point number, the result is the same: that integer can be represented exactly, as long as you don't exceed the number of bits in the mantissa, + 1 bit in the exponent.

Of course, if you try to store an actual floating-point number (e.g. 12.345) in a floating point representation, all bets are off, so your program has to be clear that the number is really a genuine integer that doesn't overflow the mantissa, in order to treat it like an actual integer (i.e. with respect to comparing equality).

If you need more integer precision than that, you can always employ an arbitrary-precision library.

Further Reading
What is the maximum value of a number in Lua?

It's not going to hurt to build an actual computation that would fail. Division and multiplication can be used to reliably produce the kind of values you are looking for. However, once you've calculated interesting values to compare, what's the point of recalculating them each time? Do you want to unit test the calculations?

One thing to consider is that numbers like 0.2 cannot be represented exactly in floating point. Using something like that as your threshold value could potentially produce some unexpected results. Numbers such as 0.5, 0.25. 0.125 are exact in floating point. You might want to come up with unit tests check these situations where the threshold itself is a estimate.