Each year around this time I am both amazed and dismayed at the poor numeracy skills of some of our undergraduate students. (Particularly bearing in mind that we don't exactly have soft entry requirements.) To be honest, it's not the bad numeracy alone that upsets me - it's when common sense fails to pick up blatant bad numeracy. In particular, I am talking about spontaneous DNA mutation rates in humans during DNA replication.
The key is the superscript. A little thing but a big effect. The spontaneous error rate during human DNA replication is on the order of (and frequently quoted as) 1 mutation every 1010 bases. (Bionumbers has the rate at 5 x 1011, which is close enough.) For those not familiar with powers, that's 1 in 10,000,000,000. It is most certainly not 1 in 1010. And yet, every year, a number of students confidently assert that the spontaneous mutation rate is 1 in 1010 bases. To put this in context, we have approx 3 x 109 (3 billion) bases in our genome. This means that each time our genome is replicated, there is (on average) less than one mutation. If, on the other hand, the mutation rate was 1 in 1010, there would be getting on for 3 million mutations per replication. We'd be dead. (Actually, 3 billion bases is our haploid genome size and we're diploids, so we'd actually get twice as many mutations, including about 3000 affecting both copies.)
Another way to put that in perspective. Imagine that DNA was scaled up so that each nucleotide was one mm. On average, human DNA polymerase could copy DNA from the North Pole to the Equator before it made a mistake. This is approx. ten "Megametres", or 1010mm. (The metre was originally defined to be one ten millionth of this distance. Not really sure why. I guess it seemed like a good idea at the time. Anyway...) If the error rate was 1 in 1010, it probably wouldn't even make it out of the room - just over 1m. Supercripts: they're important!
(Because of the number of germline cell divisions involved in making eggs and sperm, the human per generation mutation rate is about 2.5 x 108 - or a 100ish mutations per generation. Imagine if that was a billion! In real life, the polymerase would make it about 6m versus 0.6µm before making a mistake. That's still pretty impressive when you think how tiny it is! It would take a single polymerase about about 9.6 years to replicate the 6m, though! Just as well we make a whole bunch of them...)