How is it possible that when you divide 1 by 9,899, you get two-digit Fibonacci numbers also being carried, etc.?

Question

When I divided $1$ by $9,899$, I got two-digit Fibonacci numbers also being carried: $0.0001010203050813213455904636\dots$

When I divided $1$ by $89$, I got one-digit Fibonacci numbers at the beginning: $0.0112359\dots$ (there was originally an eight, but there was carrying and it changed to a nine)

How does all of this happen? There is more than this, you know. What do you think is going on here?

score 1 · Accepted Answer · edited Apr 01 '20 at 19:15

1

This happens because the generating function of the Fibonacci numbers is $\frac x{1-x-x^2}$. At $x=0.01$, this is $\frac {100}{9899}$.

edited Apr 01 '20 at 19:15

user729424

5,061

answered Nov 30 '14 at 15:42

Ross Millikan

374,822

How is it possible that when you divide 1 by 9,899, you get two-digit Fibonacci numbers also being carried, etc.?

1 Answers1