## Champernowne's constant

### Problem 40

Published on Friday, 28th March 2003, 06:00 pm; Solved by 53973; Difficulty rating: 5%An irrational decimal fraction is created by concatenating the positive integers:

0.123456789101112131415161718192021...

It can be seen that the 12^{th} digit of the fractional part is 1.

If *d*_{n} represents the *n*^{th} digit of the fractional part, find the value of the following expression.

*d*_{1} × *d*_{10} × *d*_{100} × *d*_{1000} × *d*_{10000} × *d*_{100000} × *d*_{1000000}