# Are all rational numbers normal?

1. Nov 17, 2014

### gummz

2. Nov 17, 2014

### HallsofIvy

Staff Emeritus
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!

3. Nov 17, 2014

### Orodruin

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

4. Nov 17, 2014

### 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?