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It's over the head of everyone. That's why I shared it here.
No, but 0.899... = 0.9. This only applies to the repeating sequences of the last digit of your base. We're using base 10 so it got to be 9.
Then you split the leftover dog into 10 parts. Why 10? Because you use base 10. Three of those parts go to each lot of dogs... and you still have 1/10 dog left.
Then you do it again. And you have 1/100 dog left. And again, and again, infinitely.
If you take that "infinitely" into account, then you can say that each lot of dogs has exactly one third of the original amount.