(This article was first published on

**Human Mathematics**, and kindly contributed to R-bloggers)Here’s the distribution of the first million digits of the square root of two’s decimal expansion.

`Number of digits | is:`

0's | 99 818

1's | 98 926

2's | 100 442

3's | 100 191

4's | 100 031

5's | 100 059

6's | 99 885

7's | 100 012

8's | 100 347

9's | 100 126

If each digit had a Bernoulli chance of coming up (like a 10-sided die), you’d expect to see 10 000 ± 30 times. And going on with that same assumption, the chance of the least-frequent digit coming up less than 99 000 times would be something like one percent.

What does it mean? I will meditate on this and expand √2 in different bases besides 10.

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