These days terms like ‘nano-robots’ and ‘tera-bytes’ get mentioned all the time, like it’s expected that you have any idea what they really mean. And the same with money is spoken of in almost cryptic terms, a billion pounds cut from the NHS, a trillion spent on the war. It’s so hard to have any real grasp of the meaning of these words.
But they come from the same group of words as some that are really familiar to us, like ‘milli’ as in millimetre, and ‘kilo’ that we see so often in kilogramme. In fact, it seems that this familiarity has led to us forgetting what these prefixes mean, because we all know without even really thinking what they are.
To understand the terms more fully, we need to get to grips with the way that scientists write down very large and very small numbers, to save time, paper, and also to reduce the chance of error. This is called scientific notation and it means that we can write a large number like 389000000 (incidentally the number of chocolates I ate at the weekend) in a shorter form. To do this, we use powers of 10.
We’re taught from a young age that if you multiply by 10 you add a zero. 101 is 10 and 102 is 100. You can see here that the power number is the same as the number of zeros that appear. Similarly, if we go back to the number of chocolates that I ate we can see that it is nine digits long. What we’re looking for is a small number which can be multiplied by 10 to the power of something, 10? If you like.
There is a simple method for doing this. Write a decimal point after the first significant figure (in this case the 3), and then count how far you moved the decimal point from its original position. Write down the significant figures (here the 3, the 8 and the 9), with the decimal point in its new place. And follow this by 10 to the power of how many places you moved the decimal place. Long in words, but the answer is short:
3.98 x 108
But what has this got to do with nano and all that nonsense? Well, it’s just another way of doing the same thing, but with words that mean ‘10 to the power of’ rather than using the scientific notation. Let’s look at an easy example. These are all the same:
1.0 x 103 m
This is easy because we know that in km the ‘k’ part means ‘kilo’ and that one kilometre is a thousand metres. We can also go the other way, to use the symbols to show something really small. These are all the same too:
1 x 10-3 m
Again, we’re using mm, which we know is short for millimetre. It’s the milli part that means we know it’s small, one thousandth of a metre. But kilo and milli aren’t just used in the few places we’ve heard of them, they are part of a long list of abbreviations for units, each with its own symbol and friend over in the world of scientific notation.
So now you know how to understand them, it’s easy for me to explain that nano means 1 x 10-9 and tera means 1 x 1012, which is the same as a trillion. I always like to change everything into scientific notation, because from there it’s really easy to compare the powers of 10 to get a good idea of the scale of the numbers. Although I have to admit that when it comes to the number of chocolates I’ve eaten I just like it because it’s faster to write.