# billions, trillions and googolplexes

The word *billion *is now universally accepted to mean ‘a thousand million’. This usage is American in origin; the British word *billion *used to mean ‘a million million’ (ie a trillion, in today’s terms), and I have a feeling this was the case in French too. However, American linguistic imperialism has won out and we all now think of a billion as a nine-zero number. I’m not complaining about that. There’s actually a logic to it, as evidenced by this table of really big numbers, each of which is a thousand times the last:

a million – 6 zeroes

a billion – 9 zeroes

a trillion – 12 zeroes

a quadrillion – 15 zeroes

a quintillion – 18 zeroes

a sextillion – 21 zeroes

a septillion – 24 zeroes

an octillion – 27 zeroes

a nonillion – 30 zeroes

a decillion – 33 zeroes

There are estimated to be about one quadrillion ants in the world, I once read; and the Earth weighs over six sextillion tons. The last few of these numbers, though, are so huge that they are scarcely ever needed to count or measure anything on Earth.

After *decillion, *there are no named numbers, except for the* googol*, a whimsical made-up number which has a hundred zeroes after it; and then the *googolplex, *which supposedly has a googol zeroes after it. Incidentally, I have noted an interesting failure of my imagination when I try to visualise a googolplex written down. My internal dialogue goes something like this: ‘So if it was written down, how many zeroes would it have after it? – A googol. – But what does that mean? – It’s got a hundred zeroes after it. – Oh, right, so it would have a hundred zeroes? – Yeah, that’s right – no, wait a minute, that’s a googol. A googol*plex* has a googol zeroes after it. – But how many *is * a googol? – It’s got a hundred zeroes after it. – So, er…’

In fact a googolplex is impossible to visualise. You just can’t imagine what a googol zeroes written down would look like – I don’t suppose there’d be enough universe to contain a piece of paper with it written on – and that’s why I keep wanting to shrink it down to a hundred zeroes.

Well, yes, there is a logic to it, but it’s not as tidy as the old British (and French) way. For “billion” on, it used to be 1,000,000^

nwherenis the number indicated by the prefix. Now it’s 1,000 + 1,000^n, which is kinda kludgey./@

* 1,000 x 1,000

n, of course! (Or 1,000^(n+1).)