Mental calculation hacks and estimation for engineers

As I was reading the chapter on math from Mind Performance Hacks, I realized that I have already been using some mental calculation hacks mentioned in the book without knowing they are actually hacks. (This is one of the amazing things reading this book,   understanding more about my own mind.) Some hacks that I’ve been using, also mentioned in the book –


If I want to add a list of numbers, I would first rearrange them to make 10s or 5s, then add them up in tens. This is especially useful for checking bills.

eg 24+25+33+12+16 = (24+16) + (33+12) + 29 = 40 + 45 + 25 = 110

Looking for friendly numbers

Work with numbers you are more comfortable with. Instead of multiplying 29 to 7, multiply 30 to 7 and subtract 7 from the result.

Working opposite

Multiplying is always easier than dividing for me. So if I need to divide 102 by 7, I would keep multiplying 7 by a number until it exceeds 102 (find out the number of sevens in 102).  Stop at 7×15 (105) because that exceeds 102, so there are 14 sevens (98) in 102 with a remainder of 4.

Some hacks are particularly interesting, especially the part on estimation which is so useful for engineers.

Estimate orders of magnitude [Hack #41] – I like the part on “How would you move Mount Fuji”. This reminds me of what my physics professor liked to do during lecture, he used such technique to solve really weird questions like how many water molecules in a glass of water we drink were also drank by Einstein.

As an engineering student, I love the magical sign . Approximation is so useful for calculations in engineering, especially when designing circuits and devices. We often make a lot of estimations, because unlike maths, there isn’t really a “correct” answer (or we couldn’t be bothered), anything less than around 10% error is considered good. In reality every component has a tolerance, normally it’s 10% or 5% tolerance, but even with the same tolerance different manufacturers also vary a lot, components don’t come at their rated values. Surely you can get everything with very low tolerance, but what are the cost? Engineers also worry about money, a lot! I learnt this because every time when I can’t think of anything for those pros and cons questions, I would just write “expansive” under cons or “low cost” under pros, I would definitely get something (another hack maybe?).

I was so happy when I was learning to design circuits (on paper, it was a university course) because I could finally calculate using a lot of nice looking whole numbers and not press the calculator until my fingers cramp (A level math and physics, yuck!). I remember one of my professors said that in engineering everything is based on assumptions and approximations. There is always an “ideal something” and then a “real something”. Just like my grades, I make a lot of assumptions when calculating my ideal grades, which are just estimations of my REAL grades, very bad estimations… :(