I read a very basic approach to Zeno's paradox, called Achilles (it is the race between Achilles and the tortoise), where the person thought it would be a good idea to just use decimal periodicity as "counterargument".
It's part of FB posts by teachers on math to secondary school kids, so nothing strange with the actual approach. If we assume that Achilles was 10 times faster than the tortoise, and the starting advantage of the tortoise was 1 stadium (ancient greek measure for distances), it follows that for each period of concurrent movement of Achilles and the tortoise you would have the distance minimized to its 1/10 (Achilles moves) and simultaneously increased by 1/10 of 1/10 (tortoise moves). So the race would go on for 1,111... stadia, therefore you can get rid of the periodicity by setting some x=1,1..., a 10x=11,1... => 10x=1x+ 10x-1x=>9x=10*=>x=10/9= 1 stadium and 1/9 of stadium.
But the whole point of the paradox is that you are meant to see time frozen, moving only when the tortoise moves, stopping each time it stops and only then check Achilles' position=> if you allow for both moving, obviously there's a time the faster one will overtake the slower one. Being a paradox, it tells you that there are infinitely many moments when the tortoise is ahead (of course it is a converging series; it doesn't add to infinity. Yet the point in Zeno is about sets with infinitely many members).
My impression was mixed. On the one hand, it's a fine (though obviously too easy; there is only one decimal part and only that being repeated) way for kids to practice turning numbers with decimal periodicity to fractions. On the other, it belittles what Zeno presented. Imo the kids would be better served if there was explanation of why the fractional form means that decimal periodicity in some cases (eg 0.999... or 0.333...), due to always being in tautology with the ratio of linked integers, has certain implications (eg 0.999....=1).
*10= 11,1... -1,1...