Mathematical probabilities can get a little confusing (or annoying) sometimes. So with that in mind, here is some information:

A 1% drop rate means that each individual FATE that you complete, you have a 1 in 100 chance to see the Atma drop. In other words, whether it's your first FATE or your 500th FATE, your chance to see it on that FATE is 1%.

You have a...

...25% chance to see it drop within 28 FATEs.
...33% chance to see it drop within 40 FATEs.
...50% chance to see it drop within 68 FATEs.
...66% chance to see it drop within 109 FATEs.
...75% chance to see it drop within 138 FATEs.
...99% chance to see it drop within 458 FATEs.

No amount of FATEs gives you a 100% chance to see the Atma.

(cheers to Razztra for his maths)