We're dividing 102240 by 13 
We want to divide 102240 by 13.

Going ahead to step 1:
When dividing 1 by 13, we get 0 with a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 13

Going ahead to step 2:
10 divided by 13 is 0 with a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 10, we get 10.
Append the next digit (2) from the dividend to 10 and continue with: 102 / 13

Going ahead to step 3:
The number 13 fits into 102 7 times, leaving a remainder of 11.
Use 7 as the next digit of our solution. 
Result so far: 7.0
Deduct 91 from 102 and we're left with 11.
Append the next digit (2) from the dividend to 11 and continue with: 112 / 13

Advancing to step 4:
112 divided by 13 is 8 with a remainder of 8.
The number 8 becomes the next digit in our result. 
Result so far: 78.0
Deduct 104 from 112 and we're left with 8.
Bring next digit (4) of the dividend behind the 8 and repeat the process: 84 / 13

Going ahead to step 5:
If we divide 84 by 13, we get 6 and a remainder of 6.
Put 6 as the next digit of the answer. 
Result so far: 786.0
The remainder is 6 after subtracting 78 from 84.
Bring next digit (0) of the dividend behind the 6 and repeat the process: 60 / 13

On to step 6:
60 divided by 13 is 4 with a remainder of 8.
Write down 4 as next digit of the result. 
Result so far: 7864.0
If we subtract 52 from 60, we 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.

Moving on to step 7:
The number 13 fits into 80 6 times, leaving a remainder of 2.
Put 6 as the next digit of the answer. 
Result so far: 7864.6
The remainder is 2 after subtracting 78 from 80.
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 8:
13 can be fit into 20 1 times, resulting in a remainder of 7.
Use 1 as the next digit of our solution. 
Result so far: 7864.61
If we take 13 away from 20, we end up 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 9:
When dividing 70 by 13, we get 5 with a remainder of 5.
The next digit of our result is 5. 
Result so far: 7864.615
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.

On to step 10:
The number 13 fits into 50 3 times, leaving a remainder of 11.
Record the quotient 3 as the next digit in the result. 
Result so far: 7864.6153
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 11:
13 can be fit into 110 8 times, resulting in a remainder of 6.
The next digit of our result is 8. 
Result so far: 7864.61538
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 12:
The number 13 fits into 60 4 times, leaving a remainder of 8.
Use 4 as the next digit of our solution. 
Result so far: 7864.615384
Deduct 52 from 60 and we're left with 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 13:
If we divide 80 by 13, we get 6 and a remainder of 2.
The next digit of our result is 6. 
Result so far: 7864.6153846
The remainder is 2 after subtracting 78 from 80.
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 14:
When dividing 20 by 13, we get 1 with a remainder of 7.
Record the quotient 1 as the next digit in the result. 
Result so far: 7864.61538461
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.

The final result is 7864.61538461 with a remainder of 7e-09.