Natalie Angier in The New York Times:
Grim though the economic spur may be, some scientists see a slim silver lining in the sudden newsiness of laughably large numbers. As long as the public is chatting openly about quantities normally expressed in scientific notation, they say, why not talk about what those numbers really mean? In fact, they shamelessly promote the benefits of quantitative and scientific reasoning generally. As they see it, anyone, no matter how post-scholastic or math allergic, can learn basic quantitative reasoning skills, and everyone would benefit from the effort — be less likely to fall for vitamin hucksters, for example, or panic when their plane hits a bumpy patch.
One excellent way to start honing such skills is with a few so-called Fermi problems, named for Enrico Fermi, the physicist who delighted in tossing out the little mental teasers to his colleagues whenever they needed a break from building the atomic bomb.
Here is how it works. You take a monster of a ponder like, What is the total volume of human blood in the world? or, If you put all the miles that Americans drive every year end to end, how far into space could you travel? and you try to estimate what the answer might be. You resist your impulse to run away or imprecate. Instead, you look for a wedge into the problem, and then you calmly, systematically, break it down into edible bits. Importantly, you are not looking for an exact figure but rather a ballpark approximation, something that would be within an order of magnitude, or a factor of 10, of the correct answer. If you got the answer 900, for example, and the real answer is 200, you’re good; if you got 9,000, or 20, you go back and try to find where you went astray.