Let's divide 103071 by 13
Our goal is to divide 103071 by 13.

Going ahead to step 1:
If we divide 1 by 13, we get 0 and a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 13

On to step 2:
13 can be fit into 10 0 times, resulting in a remainder of 10.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 10 leaves us with 10.
Grab the next digit (3) from the dividend, add it to 10, then carry on: 103 / 13

On to step 3:
13 goes into 103 7 times with a remainder of 12.
Use 7 as the next digit of our solution. 
Result so far: 7.0
The remainder is 12 after subtracting 91 from 103.
Append the next digit (0) from the dividend to 12 and continue with: 120 / 13

Step 4:
If we divide 120 by 13, we get 9 and a remainder of 3.
The next digit of our result is 9. 
Result so far: 79.0
Subtracting 117 from 120 leaves us with 3.
Include the next digit (7) from the dividend after 3, then repeat: 37 / 13

Let's proceed to step 5:
37 divided by 13 is 2 with a remainder of 11.
Use 2 as the next digit of our solution. 
Result so far: 792.0
Subtract 26 from 37 to get 11.
Grab the next digit (1) from the dividend, add it to 11, then carry on: 111 / 13

Moving on to step 6:
13 can be fit into 111 8 times, resulting in a remainder of 7.
The next digit of our result is 8. 
Result so far: 7928.0
Deduct 104 from 111 and we're left 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.

On to step 7:
If we divide 70 by 13, we get 5 and a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 7928.5
Subtract 65 from 70 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 8:
When dividing 50 by 13, we get 3 with a remainder of 11.
The number 3 becomes the next digit in our result. 
Result so far: 7928.53
Subtract 39 from 50 to 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.

Moving on to step 9:
When dividing 110 by 13, we get 8 with a remainder of 6.
Record the quotient 8 as the next digit in the result. 
Result so far: 7928.538
The remainder is 6 after subtracting 104 from 110.
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 10:
13 can be fit into 60 4 times, resulting in a remainder of 8.
Put 4 as the next digit of the answer. 
Result so far: 7928.5384
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 11:
13 goes into 80 6 times with a remainder of 2.
Record the quotient 6 as the next digit in the result. 
Result so far: 7928.53846
If we take 78 away from 80, we end up 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.

Going ahead to step 12:
13 can be fit into 20 1 times, resulting in a remainder of 7.
The next digit of our result is 1. 
Result so far: 7928.538461
Deduct 13 from 20 and we're left 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.

Moving on to step 13:
The number 13 fits into 70 5 times, leaving a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 7928.5384615
Subtracting 65 from 70 leaves us 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 14:
50 divided by 13 is 3 with a remainder of 11.
Put 3 as the next digit of the answer. 
Result so far: 7928.53846153
If we take 39 away from 50, we end up with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Our division results in 7928.53846153 with a remaining 1.1e-08.