More on 0.9999... = 1!

When the internet talks about 0.9999 equals 1, how many nines do they use? Here's a graph of exactly that.

Number of nines in "0.999999", etc, as reported by Google.

While there is a bump at 9, people seem to think that 9 nines is nice and symmetric, there isn't a bump at 10. There is also a bump at 32, a nice power of two.

Of course, this plot should remind you of this:

One more thing.

At the end of the last post,  I asserted that:
\[\sum_{i = 1}^{\infty} \frac{1}{2^i}\] also converges to 1. It's an interesting fact that in base two, 0.1111... = 1. In fact, for every base b, you can represent one as an infinite sequence of \((b-1)\)s.