The 0's don't give you anything. You could just say 1. As for why they're equal, there are various proofs and explanations, but the simplest proof is probably:

The 0's don't give you anything. You could just say 1. As for why they're equal, there are various proofs and explanations, but the simplest proof is probably: 1/3 + 1/3 + 1/3 = 1 0.333... + 0.333... + 0.333... = 1 0.999... = 1