Spot on. I would add to this explanation that the real confusion comes from the fact that in most languages when you write `0.1`, it doesn't mean 0.1 = 1/10 – instead it means the closest number to 0.1 of the form n/2^k where n < 2^53. Namely 0.1000000000000000055511151231257827021181583404541015625, which we can represent in decimal because 2 divides 10. And, of course, the illusion that `0.1` is actually 0.1 is supported by the great efforts [1] made to print floating-point values with the least number of digits necessary to reproduce them, so `0.1` still looks like 0.1 when you print it even though it isn't.

[1] http://www.cs.tufts.edu/~nr/cs257/archive/florian-loitsch/pr...