# Dividing by 63

At a recent MathsJam, @brownmaths – who really should have known better – showed up with a calculator. Dear oh dear.

His excuse was that it was in his teaching satchel, and he sometimes needed it to work out trigonometric functions (the Mathematical Ninja rolled his eyes, but I said fair enough) or “If there’s a test and it’s out of 63, and I need to work out the percentages…”

“Divide by 7, then by 9” was the obvious response from the gathering, but I wondered if there was a nicer way.

63 is reasonably close to 62.5, which is 500/8. That suggests that multiplying the raw scores by 16 and dividing by 10 should give you a pretty good approximation for the percentage score. (Since $63\times16=1008$, the answer will be 0.8% too high - which you can adjust for.)

For example, it’s a tough test, and someone has managed 19/63. $19 \times 16 = 304$, so that’s about 30% (which makes sense – 21/63 is a third). You could then take off 0.8 for every hundred – subtracting 2.4 gives 301.6, which you turn into 30.16%. In fact, it’s $30.\dot 15873\dot 0$, so not bad.

Let’s say a better student has 58/63. That’s harder to multiply by 16, but not that hard – double it, it’s 116, and $116 \times 8$ is 928 (I did 888 + 40). Now to lose 0.8 for every hundred, which is 7.2, or – if you feel like showing off, 7.4, as you have nine-and-a-quarter hundreds. That makes it 92.06% – and again, it’s bang on to two decimal places.

* Edited 2015-03-26 for clarity. * Edited 2016-06-05 to fix LaTeX