[jonmrodriguez]

At least in electrical engineering, we use mental math every day. More specifically, we use approximate mental math (trying to calculate to within about +/- 25% of the correct value) because it's faster than calculating the exact answer when we need a rough estimate of a power, current, voltage, or impedance number. I imagine that fast, approximate mental math is similarly useful in other engineering disciplines.

[ajford]

I was taught the importance of this in my first year of Physics undergrad. Fermi approximations (or order of magnitude estimation), from Fermi problems (https://en.wikipedia.org/wiki/Fermi_problem).

It is a highly valuable skill in STEM fields in my opinion. Sometimes knowing a rough number can tell you what to expect, and can immediately indicate whether something is wrong (or could go wrong).

[alwaysdoit]

One of the most important things I learned from my EE prof was that pi is 3. The square root of 10 is also 3. If you need more exact calculations, you should do it algebraically and then plug in numbers to a calculator, but for quick feasibility/sanity checks, approximate mental math is a very useful tool.

[ThrustVectoring]

Approximate mental math is really good for doing Fermi estimates, too.