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…)

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.