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Catalyst: Graham's number

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Ron Graham stands in front of image of a galaxy
Catalyst: Graham's number

SUBJECTS:  Maths

YEARS:  7–8, 9–10


If you were asked what the biggest number you can think of is, what would you say? Infinity?

Well, what about the biggest finite number you can think of?

Mathematician Ron Graham came across such a gigantic number in his research that, to capture its massive size, he and his colleagues needed to come up with new methods of notation.


Things to think about

  1. 1.What is the biggest number you can think of? One million is 1,000,000, which in exponential form is 1 x 10^6 How do we write one trillion? How can we write one trillion in exponential form?
  2. 2.What is the number called 'Graham's number'? How does Simon use trillions to demonstrate the hugeness of Graham's number? How does writing a number in exponential form help in writing a large number? What is an example?
  3. 3.You can write 2 to the power of 2 to the power of 2 in exponential form as 2^(2^2). How much is this equivalent to 8, 16, 32 or 64? Hint: first work out the powers in brackets and see that 3^(3^3) is a much bigger number. What is it and why is it so much bigger than 2^(2^2)?
  4. 4.Find some large numbers such as the mass of the Sun, average distances in km from the Sun to various planets. Write these numbers, together with their exponential form. Find out what the 'astronomical unit' AU is and how it's used for measuring distances in space. How is this written in exponential form?


Date of broadcast: 25 Oct 2012


Copyright

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