The power of estimation is indeed useful in the engineering field to simple calculations or checking whether an answer is sound or not. In actuarial sciences, one needs to be good at estimating cashflows and trends where as in finance, estimation is useful to make sure that you do not miss any zeros. As such, Fermi questions can be treated as order of magnitude questions.
If you are applying to any of those fields, you will most likely be asked to estimate some things so the best way to prepare is
1) Get a grip on the scale of things. You can do this mainly by grabbing numbers out of the things you read. Indeed, having a slight knowledge on the numbers in real life will be at your advantage against people who do not know.
For example, market capitalisation of Google is $200bil or the size of the earth is about 40,000km circumference. HOw about the power a lightbulb is about 40watts.
2) To really impress your interviewer, you must be able to also use these numbers in creative ways.
Instead of saying the US economy is worth $1 trillion, you can say, the US ecnomy is worth 5 times the market cap of Google, or instead of saying that the cables in this city sums up to 120,000km you can say that the amount of cables in this project can to 3 times around the Earth.
Not only does using Fermi approximations help you to picture your thoughts to someone, it also makes things more interesting in the conversation. No doubt, it is an important skill to keep!
Next up, how to answer interviewers when they ask what is the biggest mistake you ever made?
Objective of the interview
Things to prepare
At the Interview