my back-of-envelope system design numbers were off by three orders of magnitude and the interviewer didn't care

I said 10,000 QPS when the real number for the scenario was closer to 10 million. Panicked for a second, then just said 'let me redo this, I think I'm off' and walked through the math again out loud. Got an offer. I think they were testing whether I'd notice and fix it more than whether I nailed it first try.