Measurement: Numbers

This page is basically about the prefixes used in metric numbering systems. Questions on this subject typically come in the form of:

"What is the SI prefix meaning ten to the power of … " (or something less precise!)

or "How many millions are there in a trillion?"

Confusion is inevitable in the latter instance: most people (if not everyone) would agree that a trillion is a million billion, but what's a billion – is it a thousand million, or a million million?

The layman often believes that in Britain a billion is a million million, while in America it's a thousand million.  But this is only part of the truth – and it's also out of date.

Wikipedia comes to the rescue here by describing a "long scale" and a "short scale" (see below). Essentially (according to Wikipedia), the "short scale" is used in English–speaking countries, while the "long scale" is used everywhere else (including continental Europe) and was used in the UK up to 1974. Naturally, each language has its own equivalent of the words listed here under "long scale".

				Short scale (English–speaking countries)		Long scale (Everywhere else)		SI prefix
10–24				Septillionth		Quadrillionth		Yocto–
10–21				Sextillionth		Trilliardth		Zepto–
10–18		Million million millionth		Quintillionth		Trillionth		Atto–
10–15		Thousand million millionth		Quadrillionth		Billiardth		Femto–
10–12		Million millionth		Trillionth		Billionth		Pico–
10–9		Thousand millionth		Billionth		Milliardth		Nano– (Greek nanos, a dwarf)
10–6		Millionth						Micro–
10–3		Thousandth						Milli–
102		Hundred						Hecto– (esp. –litre, –gram)
103		Thousand						Kilo–
106		Million						Mega–
109		Thousand million		Billion		Milliard		Giga–
1012		Million million		Trillion		Billion		Tera– (formerly megamega–)
1015		Thousand million million		Quadrillion				Peta–
1018		Million million million		Quintillion				Exa–
1021		(You get the idea …)		Sextillion				Zetta–
1024				Septillion				Yotta–

Another term that causes confusion is the googol, and more so the googolplex.

Term for 10100 – ten to the power of one hundred, written as a one followed by 100 zeroes		Googol
Ten to the power of a googol (1 followed by a googol of zeroes)		Googolplex

In case you didn't already know, a googol is a very big number.  For example, the number of atoms in the observable universe is estimated to be around 10 to the power 80.  (Actually between 10⁷⁸ and 10⁸².)  In other words, to have a googol of atoms you would need about 10²⁰ universes – or a hundred quintillion (that's a hundred million million million – see above!

And that's just a googol.  A googolplex is a really stupidly high number.  It's much, much bigger than a googol squared, or a googol of googols (which is the same thing) – that would be ten to the power of 200.

The number of googols in a googolplex is ten to the power of (a googol minus one hundred). A hundred is so much smaller than a googol that trying to work out the number of googols in a googolplex makes my brain hurt – and I had a scientific education. In other words, my advice is – don't even go there!

The point is, however, that the googol is not really all that significant in science. It was invented by the American mathematician Edward Kasner for his book Mathematics and the Imagination, which was published in 1940. He used it to illustrate the difference between a very large number and infinity.  Kasner describes in the book how the term was coined by his nine–year–old nephew Milton Sirotta, and also how Milton suggested the term googolplex, meaning "one, followed by writing zeroes until you get tired".  Kasner decided to adopt a more formal definition.

If you were to write down a googol, it would look like this:

10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000

It has been estimated that you could never write down a googolplex as a number, because there isn't enough space in the universe.

The Googleplex, by the way, is in Silicon Valley, California – it's the headquarters of Google, Inc.

© Haydn Thompson 2017