Let's divide 17118 by 13
Our goal is to divide 17118 by 13.

Advancing to step 1:
13 goes into 1 0 times with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Take the next digit (7) from the dividend and append it to 1, then repeat: 17 / 13

On to step 2:
17 divided by 13 is 1 with a remainder of 4.
Put 1 as the next digit of the answer. 
Result so far: 1.0
If we take 13 away from 17, we end up with 4.
Fetch the next digit (1) from the dividend, attach it to 4 and continue: 41 / 13

Let's proceed to step 3:
The number 13 fits into 41 3 times, leaving a remainder of 2.
Use 3 as the next digit of our solution. 
Result so far: 13.0
Subtract 39 from 41 to get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 13

Moving on to step 4:
13 goes into 21 1 times with a remainder of 8.
The number 1 becomes the next digit in our result. 
Result so far: 131.0
If we subtract 13 from 21, we get 8.
Grab the next digit (8) from the dividend, add it to 8, then carry on: 88 / 13

Moving on to step 5:
13 can be fit into 88 6 times, resulting in a remainder of 10.
The next digit of our result is 6. 
Result so far: 1316.0
The remainder is 10 after subtracting 78 from 88.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 6:
When dividing 100 by 13, we get 7 with a remainder of 9.
Write down 7 as next digit of the result. 
Result so far: 1316.7
The remainder is 9 after subtracting 91 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

On to step 7:
13 can be fit into 90 6 times, resulting in a remainder of 12.
The next digit of our result is 6. 
Result so far: 1316.76
The remainder is 12 after subtracting 78 from 90.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Let's proceed to step 8:
13 goes into 120 9 times with a remainder of 3.
The next digit of our result is 9. 
Result so far: 1316.769
The remainder is 3 after subtracting 117 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

On to step 9:
30 divided by 13 is 2 with a remainder of 4.
Write down 2 as next digit of the result. 
Result so far: 1316.7692
If we take 26 away from 30, we end up with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Advancing to step 10:
When dividing 40 by 13, we get 3 with a remainder of 1.
Record the quotient 3 as the next digit in the result. 
Result so far: 1316.76923
Deduct 39 from 40 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 11:
13 goes into 10 0 times with a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 1316.76923
The remainder is 10 after subtracting 0 from 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 12:
13 can be fit into 100 7 times, resulting in a remainder of 9.
Record the quotient 7 as the next digit in the result. 
Result so far: 1316.7692307
The remainder is 9 after subtracting 91 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Let's proceed to step 13:
The number 13 fits into 90 6 times, leaving a remainder of 12.
The number 6 becomes the next digit in our result. 
Result so far: 1316.76923076
Subtracting 78 from 90 leaves us with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

The final outcome is 1316.76923076, with a leftover of 1.2e-08.