Number Theory

Let's note that 1/17 is a repeating decimal, which can make our lives quite easy!

We have

$1/17 = 0.\overline{0588235294117647}$

There are 16 repeating digits. Thus, we simplfy have

$4000/16=250$

Thus, the last digit, 7 is the 4000th digit. 

So our answer is 7. 

Thanks! :)