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## High Numbers

27 Aug

In a recent article in one of his blogs my old school friend Mike V (that’s the one in Thailand) mentions an event which if “experts” are to be believed should have had odds of 1 in (1 followed by the word “million” fifteen times) against it.

Oh go on then, you can find it at http://damienatloppers.wordpress.com/2010/08/20/damien-on-double-yolk-eggs/

As Mike may recall I was rubbish at maths at school (21% in the GCE mocks – or “A* grade” as they call it nowadays!) but I think that if you add six zeroes for each million you get a 1 followed by 90 zeroes which I don’t propose to write down!

Furthermore, I have also dragged up from the forty year old mathematical swamp in my memory that this is equivalent to 10^90 (Ten to the power Ninety) which is quite a big number.

So big in fact that Mike suggests it might be equal to the number of grains of sand on all of the beaches in the world.

I think he is wrong!

You see a few years ago I read a factual article by Isaac Asimov (who could write competently on just about anything) concerning really big numbers.  And it seemed to me that I remembered a few things that needed checking. Not having his article immediately to hand I resorted to a spot of Googling – which is quite apt, a “google” being a very large number. Look it up if you don’t believe me!

Now you will have to take some of the figures that I found on trust because “wildly inaccurate” seems to sum up the answers I was able to get from the various forums (fora?) that I looked at.

Before we get to my findings however, let’s try to get an idea of the magnitude of the numbers involved here.

One million (1,000,000) is more easily written as 10^6; one billion US style (1,000,000,000 – one thousand million) is 10^9; one billion UK style (1,000,000,000,000 – one million million) is 10^12.

And if you want to start multiplying these numbers you do it by ADDING the exponents (or “powers”) together. Thus, 10^2 (100) times 10^3 (1000) equals 10^5 (100,000) not 10^6 (1,000,000). OK?

There are varying estimates for the number of grains of sand on planet Earth (and frankly I’m not remotely interested in checking the workings of any of the geeks who presented those estimates – get a life boys!) but the nice, round figure roughly in the middle of the range is………<slow drum roll>

10^20

I looked further and found a reasonable estimate of the number of stars in our average-sized Galaxy to be 10^11 – which, strangely is also the current informed guess at the number of Galaxies in the universe.

So, remembering to ADD the exponents there are in the region of 10^22 stars in the whole universe.

And if every single one of them averages one Earth-type planet (unlikely) with a similar number of beaches then the number of grains of sand in the Universe would still only be 10^42 and we’re not even close  to that whopping great number we started with.

I really don’t want to go further without checking with the late Doctor Asimov but I think that to get nearer to the figure of 10^90 we have to start counting the number of atoms in all of those grains of sand!

Even then I have a sneaking feeling I’m being too conservative!

And I hope that my friend in Thailand’s sums will be a little more accurate when it comes to converting his UK income into Thai Baht!

Alfie

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4 Comments

Posted by on August 27, 2010 in Uncategorized

### 4 responses to “High Numbers”

1. August 28, 2010 at 5:46 pm

Ahah! My figure was INDEED 10^90 – but my “number of grains of sand on all the beaches in the World” reference was only intended as an analogy – I had no idea someone had actually ESTIMATED that (like you say, they should get a life!)

Anyhoo, if their estimate of those grains of sand is a mere 10^20, it means my eggs story was even MORE remarkable – until you look at the other data I uncovered.

While I’m on this – you must have heard this question: if you put one grain of rice on the first square of a chess board – then two grains on the second, four on the third, eight on the fourth and so on – how many grains would there be on the last square? (The standard chess board having 64 squares).

This is of course a matter of exponential growth. The answer is staggering – I once had some spare time and computed it as SEVERAL CUBIC MILES worth.

And having just Wiki-ed it, it appears I was about right – the pile of rice would be bigger than MOUNT EVEREST!

2. September 1, 2010 at 12:09 pm

You shouldn’t keep setting me these little puzzles! After reading the chessboard thing I naturally looked it up!

……and the answer is:

2^64 = 1.84467441 × 10^19

So not TOO far short of the “grains of sand” estimate!

Actually the real answer is ((2^64)-1) or 18,446,744,073,709,551,615

Don’t you find that fascinating?

No, I didn’t think so!

Alfie

3. September 7, 2010 at 2:57 pm

Huh?!?!?!?!?! Confused Arts graduate!!!!