Let's divide 135115 by 13
Our goal is to divide 135115 by 13.

Advancing to step 1:
When dividing 1 by 13, we get 0 with a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Fetch the next digit (3) from the dividend, attach it to 1 and continue: 13 / 13

Going ahead to step 2:
The number 13 fits into 13 1 times, leaving a remainder of 0.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Deduct 13 from 13 and we're left with 0.
Bring next digit (5) of the dividend behind the 0 and repeat the process: 5 / 13

Advancing to step 3:
If we divide 5 by 13, we get 0 and a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 10.0
If we take 0 away from 5, we end up with 5.
Bring next digit (1) of the dividend behind the 5 and repeat the process: 51 / 13

Let's proceed to step 4:
13 can be fit into 51 3 times, resulting in a remainder of 12.
The next digit of our result is 3. 
Result so far: 103.0
If we subtract 39 from 51, we get 12.
Take the next digit (1) from the dividend and append it to 12, then repeat: 121 / 13

Moving on to step 5:
13 can be fit into 121 9 times, resulting in a remainder of 4.
Write down 9 as next digit of the result. 
Result so far: 1039.0
The remainder is 4 after subtracting 117 from 121.
Bring next digit (5) of the dividend behind the 4 and repeat the process: 45 / 13

On to step 6:
When dividing 45 by 13, we get 3 with a remainder of 6.
Record the quotient 3 as the next digit in the result. 
Result so far: 10393.0
Subtracting 39 from 45 leaves us with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Moving on to step 7:
13 goes into 60 4 times with a remainder of 8.
Put 4 as the next digit of the answer. 
Result so far: 10393.4
Subtract 52 from 60 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Step 8:
When dividing 80 by 13, we get 6 with a remainder of 2.
Write down 6 as next digit of the result. 
Result so far: 10393.46
Deduct 78 from 80 and we're left with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 9:
The number 13 fits into 20 1 times, leaving a remainder of 7.
The next digit of our result is 1. 
Result so far: 10393.461
Subtracting 13 from 20 leaves us with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 10:
13 goes into 70 5 times with a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 10393.4615
If we take 65 away from 70, we end up with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Let's proceed to step 11:
13 goes into 50 3 times with a remainder of 11.
Put 3 as the next digit of the answer. 
Result so far: 10393.46153
If we subtract 39 from 50, we get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Advancing to step 12:
13 can be fit into 110 8 times, resulting in a remainder of 6.
Put 8 as the next digit of the answer. 
Result so far: 10393.461538
If we subtract 104 from 110, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

On to step 13:
The number 13 fits into 60 4 times, leaving a remainder of 8.
The next digit of our result is 4. 
Result so far: 10393.4615384
Subtract 52 from 60 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Let's proceed to step 14:
13 can be fit into 80 6 times, resulting in a remainder of 2.
The next digit of our result is 6. 
Result so far: 10393.46153846
Subtracting 78 from 80 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

In conclusion, the division gives 10393.46153846 with a balance of 2e-09.