If you’ve been reading the ninja secrets over the last year or so, you’ll have noticed that adjusting by percents is a big part of ninjary, but I’ve never really explained how to do it. Let me put that right.

It works pretty much as you’d expect: you work out the right percentage and add it on or take it off.

The way the Mathematical Ninja does this is normally to work out either 1% or 10% and adjust from there. For instance, to find 3%, you’d just treble 1%. To find 5%, you’d halve 10%.

Let’s say, for example, you have to work out $g \sqrt{2}$. You might say “That’s 1.4 (+1%) times by 10 (-2%) — which works out to 14 (-1%). 1% of 14 is 0.14, so that’s going to be 13.86. That’s practically spot-on.

If you know $\sqrt{\frac{1}{2}}$ is 0.7 (+1%) and $\sqrt{3}$ = 7/4 (-1%), you can say that $\sqrt{\frac{3}{2}}$ is $\frac{4.9}{4}$ — or, if you like, that the top is 5 (-2%). You get 1.25 (-2%), and spot that 2% is 0.025; 1.22 is your guess; this time the rounding breaks in your favour and you’re right to 3 significant figures.

There’s no magic to it, other than being able to hold the adjustments in your head until the end, and possibly to know your taking-away-from-1 trick. After you’ve done it a few times, you get quite used to it.