User blog comment:Rgetar/Transfinite decimal fractions/@comment-36718579-20190417170035/@comment-32213734-20190417202219

So

1/17 * 17 = 0.99999...999...999...999...... = 1

1/17 = 0.05882352941176470588235294117647...0588235294117647...0588235294117647......

Maybe rationals have finite period, not rational reals have period ω, and not reals have period larger than ω...?

If it is true, then such numbers as π, e, √2 are repeating decimals with period ω.

But I am still not sure, how transfinite parts should begin. For example, is

1/6 = 0.1666...1666...1666......

or

1/6 = 0.1666...6666...6666......

I suspect that digits should correspond not only to ordinals, but also to surreal integers, including such numbers as ω - 1, ω - 2, ... Because we already have "negative digits after point", that is digits before point. If there are negative integers, then maybe there are other surreal integers...?

(By the way, we also have not integer digits. Because n-th decimal digit of x is

abs(x / 10n) mod 10

Let x = 10. Then 0-th digit is 0, 0.5-th digit is 3, 1-st digit is 1, 1.5-th digit is 0, 2-nd digit is 0, 2.5-th digit is 0, etc.)