Long division to primitive roots?

Question

In this long divsion:

     142857
  _________
7 | 1000000
     7
    ----
     30
     28
    ----
      20
      14
     ----
       60
       56
      ----
       40
       35
      ----
        50

the top line gives the decimal expansion of $1/7$. If we read the numbers that form the remainders, we get 3, 2, 6, 4, 5, 1, which happens to be $3^k\mod 7$. Can someone explain please?

Answer 1

$10\equiv 3 \bmod 7$. The values appearing are in fact $10^k \bmod 7$ as you effectively increase the power of 10 you are looking at down the division.