The above image has been burned into my brain for 7 years now. Not for the obvious reason, I am not horrified by the bomb or awed by the power or whatever (well maybe a little bit). This image and the story behind it taught me a great lesson about physics and business while I was studying for my undergrad at the Cavendish laboratory in Cambridge.
The lesson was that you can get to within an order of magnitude of calculating the power of a nuclear bomb using that picture and a bit of common sense. The full story can be seen here: http://www.tableausoftware.com/blog/visual-analysis-zeroth-kind-geoffrey-taylor-and-bomb and I highly recommend you read it. Spending a short amount of time and really thinking through a well defined problem should give you a good idea of the answer. If the order of magnitude of the result of a test isn’t interesting to you based on that reasoning, don’t do it. Move on to the next thing. Focus on the high impact. Your time on earth is short, don’t waste it doing trivial things.
The fermi problems are also an interesting space which I consider really similar to dimensional reasoning which is just using common sense to determine a value. My favorite is “how many blades of grass are there in a front yard”. The idea being you realize the yard is something like 10m by 10m and there are something like 20 blades of grass in a cm squared so you have 10^6 cm squared and hence 20million blades of grass in that lawn give or take (feel free to correct me if I got this one wrong). The idea is that it gives you answers that are correct to within an order of magnitude. You can read more about fermi problems at the links below.
I am a huge fan of doing this common sense checking before you do projects or to make sure that a number you are quoting is right. Really great reminder from o’reilly radar (an awesome blog) to think about this stuff.