Thirteenths (Part 3/3): Secrets of the Mathematical Ninja

The final installment, the big reveal: why does the ninja trick of multiplying by 77 and finding the nine’s complement work? My friend, that is an excellent question.

The reason is this: $77 \times 13 = 1,001$. And it turns out, 1001ths are not all that hard to work out. (This is, in fact, just an extended version of the ‘adjusting fractions’ version of a previous ninja secret).

To work out $\frac{539}{1001}$, you might start by saying: that’s 0.539 (less about a thousandth). A thousandth of 0.539 is 0.000539, which — if you take it away — leaves you with 0.538461. If you do it by hand, you even see where the dropping one and using nines come from.

Even that adjustment needs adjusting - this is about one part in a million too small, which is why it recurs.

As tricks go, this is currently one of my favourites.

* Edited 2017-04-07 to add links


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.


Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Sign up for the Sum Comfort newsletter and get a free e-book of mathematical quotations.

No spam ever, obviously.

Where do you teach?

I teach in my home in Abbotsbury Road, Weymouth.

It's a 15-minute walk from Weymouth station, and it's on bus routes 3, 8 and X53. On-road parking is available nearby.

On twitter