I've run meetups on this topic twice now. Every time I do, it's difficult to convince people it's a useful skill. More words about when estimation is useful would be nice. 

In most exercises that you can find on Fermi calculations, you can also actually find the right answer, written down somewhere online. And, well, being able to quickly find information is probably a more useful skill to practice than estimation; because it works for non-quantified information too. I understand why this is; you want to be able to show that these estimates aren't very far off, and for that you need to be able to find the actual numbers somehow. But that means that your examples don't actually motivate the effort of practicing, they only demonstrate how.

I suspect the following kinds of situations are fruitful for estimation:

• Deciding in unfamiliar situations, because you don't know how things will turn out for you. If you're in a really novel situation, you can't even find out how the same decision has worked for other people before, and so you have to guess at expected value using the best information that you can find.
• Value of information calculations, like here and here, where you cannot possibly know the expected value of things, because you're trying to decide if you should pay for information about their value.
• Deciding when you're not online, because this makes accessing information more expensive than computation.
• Decisions where you have unusual information for a particular situation -- the internet might have excellent base-rate information about your general situation, but it's unlikely to give you the precise odds so that you can incorporate the extra information that you have in this specific situation.
• Looking smart. It's nice to look smart sometimes.

Others? Does anyone have examples of when Fermi calculations helped them make a decision?