We’ll look at ways of making big numbers today. Hopefully you know about powers of numbers. Most of the biggest numbers you’ve seen probably involve powers. Powers are typically thought of as ’repeated multiplication’. You could think of this as being similar to how multiplication is ’repeated multiplication’.
We might use powers when decimal representation is far too long to be useful for understanding the size of an object.
But what if powers aren’t helpful enough? Mathematician and computer
scientist Donald Knuth introduced Knuth’s up-arrow notation. A single
up-arrow means ‘raise to the power of’. So
A million is
A couple of these problems are Fermi problems, named after physicist Enrico Fermi. This is where you try to estimate a quantity in the real world. We’re not expecting an exact answer (indeed, we don’t know the exact answer), but using some intelligent estimation, you can get a good idea of the answer.