Secrets of the Mathematical Ninja: How to be a g-whizz

The gravitational constant, as has been drilled into your head repeatedly, is 9.8 metres per second squared. It’s usually easiest to do all your sums with a $g$ in (I find it better to write $12g$ rather than 117.6, especially when the $g$s all cancel out) — but sometimes, you just want to show off.

And what better way to do that than to come up with a reasonable approximation for mechanics problems?

The basic approximation

First, the most obvious approximation: $g$ is pretty close to 10. You can come up with a pretty decent idea of the answer by just mentally replacing every $g$ with 10. That’s acceptable for a trainee mathematical ninja, but you can do better than that.

The true mathematical ninja treats $g$ as 10 (less 2%) — which is exactly how I worked out the $12g$ sum earlier: it’s 120 (less 2%), and 2% of 120 is 2.4.

Dividing with flair and panache!

If you want to divide by $g$, that's also easy: just add 2% and then divide by 10 (or add the percents last if you like) — $\frac{5}{9.8}$ is close to 0.51. (More precisely, it's: 0.51020408…, but correct to within 0.04% isn’t too bad if you ask me. If you look at the pattern, by the way, you can see echoes of the binomial expansion...)

Your root to success

The square root of $g$ is about $3.13$ (because I know $\sqrt{10} = 3.16$ and $\sqrt{9.8}$ is about 1% below that), but you can pretty much approximate it as $\pi$ ($\frac{22}{7}$ isn’t a bad estimate). You don't come across the square root all that often, but when you do, you'll look like a rockstar.

If you just learn these three tricks, they'll help you look awesome in your M1 class.


Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.


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