Thursday 11 June 2009

How high would the stack be if you piled on 1 trillion £5 notes on top of each other?

A £5 note, or indeed and bank note, is normally printed on pretty thick paper. I suppose this is so the notes don't wear out and that they are easily identified as currency, can hold a water mark and have that silver bit of metal sewn into them. So a perfectly new note fresh from an ATM would probably be about .10 of a mm thick I would imagine. However this is not easy to estimate for example it could be .5 mm thick or .2 mm thick. I really cant tell just from looking at a note and not having any knowledge of paper thicknesses and estimating on this basis would leave too big a margin for introducing a compounding error.

What I do remember is paying for a car once using cash. The fellow selling me the car insisted on me paying cash which I thought was strange in this day and age but anyway I wanted the car so and so I went into the bank and asked them to give to me £6.5k in cash. When they gave the cash to me I remember they gave it to me in used £10 notes which were wrapped up in bundles of £1000. Each £1000 bundle was about an inch thick or in metric 2.54 cms. So the entire stack was 6.5 inches or 16.5 cms. So I had around 650 ten pound notes and the hight of the stack was around 16.5 cms.

Now a trillion as far as I know is a thousand billion and a billion is a thousand million. So a million is written 1,000,000 (6 0's) A billion would therefore be 1,000,000,000 and a trillion 1,000,000,000,000. I think in scientific notation a trillion would look like 1 x 10 to the power of 12.

Now we will assume for arguments sake that there is no difference in thickness between a £10 and a £5 note. So if we divide 1,000,000,000,000 / 650 we get 1,538,461,538.

Now we multiply the 1,538,461,538 x 16.5 = 25,384,615,385.

So we have a stack 25,384,615,385 cms tall or 25,384.6 kilometers high.

The other assumption is of course that we are using used notes and that they are tied up in bundles. Also we are discounting any impact of the weight of the notes on top crushing the notes below so this would no doubt have an impact on the final measurement.

(I have tried to look up the size of a £5 note. The bank of England has some useful data on the size of the notes but not on the width. Various internet sources claim a dollar bill is 0.0043 inches thick or 0.10922 mm. Assuming a £5 note is about the same we get 0.10922 x 1 x 10 to the power of 12 = 109.220 kilometers. So with the estimate of 25k kilometer I was out by 84 kilometers. A fair distance off but will within Fermi's order of magnitude!)

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