Unfortunately, a lot of calculators are going to truncate the results. However, if you manage to get a hold of one that doesn’t, solving 1/998001 will generate all the three digit numbers from 000 to 999. And in order, no less. I have no idea how this works, but it’s a pretty neat trick and even a bit unsettling. If you’re a fan of this kind of spooky math fun, solving 1/9801 will generate all the consecutive two digit numbers.


If you notice that 998001 is 999 squared, you can see the reason why.

1/998001 = 0.000001 x 1/(1-0.001)^2.

Then if you use the power series expansion 1/(1-x) = 1+x+x^2+x^3+… this means
1/998001 = 0.000001 x (1+0.001+0.001^2+….) x (1+0.001+0.001^2+…)
and so you can count the number of ways to get a certain power of 0.001 in this product…


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