Number Theory

Let's first take a look at the fraction 1/17. 

It has 16 repeating digits in the form of $0. \overline{0588235294117647}$

We simplfy have to find which digit the 4000th lies on. 

First, let's do 4000/16. 

We get

$4000/16=250$

So the 4000th digit is the last digit of the repeating decimal, which is 7. 

So 7 is our answer. 

Thanks! :)