Maybe it helps you to know that mistakes happen a lot. Candidates are nervous, the stakes are high -- interviewers know this. In a way, a mistake is even an opportunity to show the interviewer how you deal with it. Do you recognize it yourself? Do you get defensive? Do you deny it? Or do you deal with it professionally?
The best candidates correct themselves. For example, after saying a mistake out loud, they stop and think about it (= sanity check), and say "wait, sorry, that cannot be true" and correct the mistake. One level below, saying "the result doesn't make sense" when not knowing the root cause of the error is better than nothing. It at least shows that you still know what you're working on and/or your business judgement if you're putting the result in context.
What about the "worst case", when you made an error and didn't notice it and the interviewer points it out to you? Just be cool about it, quickly double check that he or she is right and that you really made the mistake, and admit it briefly but clearly. Correct the numbers and go on -- don't over-apologize (of course you didn't do it on purpose, no need to waste time apologizing), but also don't deny it or ignore it or try to cover it up. A quick "Oh, yes, you're right, my mistake. The correct number is ..." will do. [Here's a secret: Often, interviewers tend to only point mistakes out if they like you and want you to succeed. If it wasn't great until that point, why bother :)]
In the end, the interviews test for so much -- intellectual rigor, energy level and posture, personality, working under stress, acting on feedback, etc. Making a small mistake in a math equation really is no big deal, esp. if you figure it out yourself.
Lastly, the "allowed margin of error" differs. If you argue that 3B people live in the U.S., you have a problem. If your estimate of supermarkets in France is off by a factor of 10, you may still be fine if your approach was good. Small mistake when summing numbers up, no biggie. 3 errors in 3 different calculations is an issue.
It's simple: Consultancies want to hire people they can send to clients and charge money for. If a candidate constantly makes mistakes or makes outrageous (=stupid) claims, he is a risk to the firm as clients will not be happy.
But judging from the question it seems you're a bit too hard on yourself :)
All the best for the interviews!