We're dividing 38971 by 13 
We want to figure out the number of times 38971 can be divided by 13.

Going ahead to step 1:
3 divided by 13 is 0 with a remainder of 3.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 3 to get 3.
Take the next digit (8) from the dividend and append it to 3, then repeat: 38 / 13

Going ahead to step 2:
The number 13 fits into 38 2 times, leaving a remainder of 12.
Use 2 as the next digit of our solution. 
Result so far: 2.0
Subtracting 26 from 38 leaves us with 12.
Grab the next digit (9) from the dividend, add it to 12, then carry on: 129 / 13

On to step 3:
The number 13 fits into 129 9 times, leaving a remainder of 12.
The number 9 becomes the next digit in our result. 
Result so far: 29.0
If we take 117 away from 129, we end up with 12.
Include the next digit (7) from the dividend after 12, then repeat: 127 / 13

Advancing to step 4:
127 divided by 13 is 9 with a remainder of 10.
The next digit of our result is 9. 
Result so far: 299.0
Subtracting 117 from 127 leaves us with 10.
Include the next digit (1) from the dividend after 10, then repeat: 101 / 13

On to step 5:
13 can be fit into 101 7 times, resulting in a remainder of 10.
Write down 7 as next digit of the result. 
Result so far: 2997.0
Deduct 91 from 101 and we're left with 10.
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:
The number 13 fits into 100 7 times, leaving a remainder of 9.
Use 7 as the next digit of our solution. 
Result so far: 2997.7
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.

Advancing to step 7:
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: 2997.76
If we take 78 away from 90, we end up 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.

Advancing to step 8:
The number 13 fits into 120 9 times, leaving a remainder of 3.
Put 9 as the next digit of the answer. 
Result so far: 2997.769
Subtract 117 from 120 to get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Advancing to step 9:
30 divided by 13 is 2 with a remainder of 4.
Put 2 as the next digit of the answer. 
Result so far: 2997.7692
If we subtract 26 from 30, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Going ahead to step 10:
The number 13 fits into 40 3 times, leaving a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 2997.76923
If we take 39 away from 40, we end up 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:
When dividing 10 by 13, we get 0 with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 2997.76923
If we take 0 away from 10, we end up with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 12:
13 goes into 100 7 times with a remainder of 9.
Write down 7 as next digit of the result. 
Result so far: 2997.7692307
If we take 91 away from 100, we end up with 9.
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 13:
13 can be fit into 90 6 times, resulting in a remainder of 12.
Record the quotient 6 as the next digit in the result. 
Result so far: 2997.76923076
Deduct 78 from 90 and we're left 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 result is 2997.76923076 with a remainder of 1.2e-08.