Background: I used to be an physicist (PhD) and graduated as an engineer (applied physics). I also actively promote science with children. I am interested in th

Background: I used to be an physicist (PhD) and graduated as an engineer (applied physics). I also actively promote science with children. I am interested in the interpretation of numbers and quantities for many years. I do not like this article because it fails to - show that we do not "feel" numbers larger than a few - and that we have a tendency to think in orders of magnitude (5, a few, lots, plenty of many). To start with: "many treated 980 million and 2 billion as nearly identical". They were right, 980 million (0.98 billion) is nearly identical to 2 billion when you look at orders of magnitude. Missing this fact is one of the big problems we have at school, namely the incapacity to estimate. We fetish exact numbers (3.14) instead of telling that pi is 3, pi squared is 10 and g is 10. This way, children can understand orders of magnitude and we do not end with (real case when I was teaching) a skydiver who lands at 573.426625432423 km/h. I cannot deny that the answer is precise to the upth-st digit. Quantities such as "a million" do not make sense outside of the context. In context they just become a number, not a quantity. For instance what is the size of a hair multiplied by a million? Or a glass? I have no idea. Sure, I can estimate that a glass is 5 cm = 5 x 10^-2 m, which makes it 5 x 10^-2 x 10^6 = 5 x 10^4 m. 50 km. But I had no idea before because I don't know what "a million times" means outside of the numbers. We are good at estimating small orders of magnitude (from experience, not more than 3) and that's all. The rest is calculus and this is easy. But also detached from reality, a scientist does not ponder on 10^9. This is jst 10^9, a number.