Are all rational numbers normal?

[gummz]

This number is rational and normal, right?

http://www.wolframalpha.com/input/?i=0.01234567890123456789...

edit - You'll have to edit in the ".." because the forum doesn't recognize it as part of the link.

 

[HallsofIvy]

On the contrary, NO rational numbers are normal! I think you have a wrong idea of what a "normal number" is. A "normal number" is one such that all possible strings of digits, n digits long, occur an equal number of times. A rational number is always eventually repeating (thinking of a terminating decimal as "repeating" 0s).

The number you give is a terminating decimal with 20 digits. It contains NO strings of length 21 or higher!

 

[Orodruin]

The number you give is a terminating decimal with 20 digits. It contains NO strings of length 21 or higher!

He means $0.\overline{0123456789}$, not a terminating decimal but still not normal.

 

[gummz]

Ah, I looked at the definition more closely and now I see my misunderstanding. It must be any string of any length, not simply a digit. But this is a simply normal number, is that correct?