Zequals: the new symbol that will make us all better at sums

Maths author Rob Eastaway thinks we need to improve our skills at estimation. Here he explains why his new symbol zequals will liberate those who struggle with arithmetic

Ziggy with it: the symbol for “zequals”

Here’s a calculation for you: 33.8 x 854.29. Do it in your head. Now.

OK it’s a crazy suggestion, anyone but a calculating genius would have to
resort to a pencil and paper, or more likely a calculator, to work this out.

Yet most people are capable of getting something close to the right answer by estimating. Maybe that was what you did as soon as you saw that calculation. But if you did, then you are in the minority. Although estimation is taught in school, it’s a skill that most school-leavers tend to forget as soon as their final exam is behind them. Why bother, when a calculator is always so close to hand?

Actually, there are very good reasons why a teenager should leave school being able to estimate. Estimation develops what mathematicians like to call a “feel for numbers”. It helps you to interpret the numbers that are fed to you by politicians, the media and your financial adviser and to decide whether those numbers deserve to be challenged (as they often do).

Indeed I would go as far as to say that I am more likely to trust somebody who, when quoting a statistic in the news, says “it’s about 1,000” than somebody who says “it’s 936.82”. When I hear a number quoted to several decimal places, I suspect the person quoting it can’t see the wood for the trees.

If you don’t have a handy method for estimation, let me introduce you to one. I call it zequals, and I describe it as “ruthless rounding”. The idea is to make calculations as simple as possible so that you can ALWAYS do them in your head (as long as you know your basic times tables, at least). I call it zequals because this technique prominently features zeroes, and I write it out using the zig-zag equals sign, above. The rule of zequals is that whenever you encounter a number, you zequal it by rounding it to a single digit followed (if it is larger than ten) by zeroes.

The number 33.8 zequals 30, while 854.29 zequals 900. (When rounding a 5 in zequals, you always round it up – hence 850 zequals 900, while 840 zequals 800).

Let’s go back to that original multiplication:

33.8 x 854.29

Applying zequals it becomes:

30 x 900 = 27,000.

But wait, we haven’t finished. That answer has two non-zero digits, and in zequals we only ever want a number to have one, so the answer 27,000 gets Zequaled to 30,000.

How does this compare to the exact answer? 33.8 x 854.29 = 28,875.002. Our estimate is within 10% of the correct answer, certainly in the right ballpark.

It can feel rather liberating to suddenly be able to treat any calculation in this ruthless and cavalier fashion. You can even do it to your times tables. What’s 3 x 7? It equals 21, but it zequals 20. So 3 x 7 x 94.3 zequals 3 x 7 x 100 zequals 2000. Simples.

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Comment:

This is something that I have done for years; a habit I got off my father.

Although, I don’t agree with the final zequals step. My original ‘guesstimate’ (as I always called it) of the above calculation was 27,000,  closer to the real answer on the other side.

 

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