In his fight against Bloodthirsty Muscular, Deku hits a 1000,000% One for All punch when we haven’t seen even All Might use that much power. How can this be possible?
It was confirmed by the Author that it wasn't actually 1000,000%. Deku said that to pump himself up.
This is explained in this article, as well as the image below:
In the last episode of My Hero Academia (Season 3, episode 8) , they gave an explanation for this (spoilers)
According to the doctor who cured Midoriya from his battle with muscular, when Midoriya says "100%" he would be using 80% of his power that's the upper limit a person can use in normal situations, and when Midoriya says 1,000,000%, he was using 100% of his power which is a power only a person can use when he is in an extreme situation, something that makes any person (including Midoriya) being bad injured after because no person is capable of using 100% of his power without hurting itself, that's why a person can only use 80% of his power in normal situations for not hurting his own body