7/22

To divide this, first we find the integer portion of the answer 7/22 = 0.  7%22 = 7, and we use 7 to find the decimal portion of the answer:

Make an array:

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
-1's across the board

7 is the remainder we've come across, I will put a 0 in position 7.

(So the array is all -1's EXCEPT that A[7] is 0.)

Now I compute 7*10 % 22.  70 %22 = 4.  Set A[4] to 1.
7*10 / 22 = 70/22 = 3.  Append to the answer string:  "3"

My new remainder is 4.

4*10%22 = 40%22 = 18.  A[18] to 2.
4*10/22 = 40/22 = 1.  Append to the answer string:  "31"

My new remainder is 18.
18*10%22 = 180%22 = 4.  A[4] has already been used.  It's not -1 anymore, it's 1.
18*10/22 = 180/22 = 8.  Append to the answer string:  "318"

Since I have a repeated remainder, I don't do many division.  Since A[4] = 1, There is one in the answer string that comes before the (.

"3(18)"

The integer answer was 0, so the total is now 0.3(18)



Compute 17/7:

Integer division  17/7 = 2.  17%7 = 3, so this will be our starting remainder.

Initialize an array of size 7 to all -1's

Set A[3] to 0.

3*10/7 = 30/7 = 4  Answer string:"4"
3*10%7 = 30%7 = 2  Set A[2] to 1.

2*10/7 = 20/7 = 2  Answer string:"42"
2*10%7 = 20%7 = 6  Set A[6] to 2.

6*10/7 = 60/7 = 8  Answer string:"428"
6*10%7 = 60%7 = 4  Set A[4] to 3.

4*10/7 = 40/7 = 5  Answer string:"4285"
4*10%7 = 40%7 = 5  Set A[5] to 4.

5*10/7 = 50/7 = 7  Answer string:"42857"
5*10%7 = 50%7 = 1  Set A[1] to 5.

1*10/7 = 10/7 = 1  Answer string:"428571"
1*10%7 = 10%7 = 3  But A[3] is already 0, it's not -1 anymore.

Since A[3] is 0, there are 0 characters before the (.

2.(428571)