Zequals and the Art of Estimation

In this Numberphile video Rob Eastaway presents Zequals which can be useful if you need to compute a quick estimate, for example to find out if your calculation is on the right track.

The idea is to ruthlessly round every number to just one significant digit. For example:

3 * 7 = 21 zz 20
7 * 8 = 56 zz 60
436 * 68 zz 400 * 70 = 28000 zz 30000

The actual answer is 29648 and surprisingly close to the zequal result of 30000. Not all numbers turn out to be that close, but this method works really well for some ranges as this graph illustrates. There’s also extra footage and more to read about zequals on Brady Haran’s Blog or Rob Eastaway’s website.