We look at the division of 13271 by 97 
Our goal is to divide 13271 by 97.

Step 1:
The number 97 fits into 1 0 times, leaving a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Fetch the next digit (3) from the dividend, attach it to 1 and continue: 13 / 97

Let's proceed to step 2:
If we divide 13 by 97, we get 0 and a remainder of 13.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 13 and we're left with 13.
Include the next digit (2) from the dividend after 13, then repeat: 132 / 97

On to step 3:
97 can be fit into 132 1 times, resulting in a remainder of 35.
The next digit of our result is 1. 
Result so far: 1.0
Subtract 97 from 132 to get 35.
Include the next digit (7) from the dividend after 35, then repeat: 357 / 97

Moving on to step 4:
357 divided by 97 is 3 with a remainder of 66.
Use 3 as the next digit of our solution. 
Result so far: 13.0
The remainder is 66 after subtracting 291 from 357.
Include the next digit (1) from the dividend after 66, then repeat: 661 / 97

Moving on to step 5:
97 goes into 661 6 times with a remainder of 79.
Write down 6 as next digit of the result. 
Result so far: 136.0
If we subtract 582 from 661, we get 79.
Since there are no more digits in the dividend, we add a zero to the remainder making it 790, and continue the process.

Going ahead to step 6:
97 goes into 790 8 times with a remainder of 14.
Write down 8 as next digit of the result. 
Result so far: 136.8
Subtracting 776 from 790 leaves us with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Let's proceed to step 7:
When dividing 140 by 97, we get 1 with a remainder of 43.
Write down 1 as next digit of the result. 
Result so far: 136.81
Subtract 97 from 140 to get 43.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

Let's proceed to step 8:
When dividing 430 by 97, we get 4 with a remainder of 42.
Use 4 as the next digit of our solution. 
Result so far: 136.814
Subtract 388 from 430 to get 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

On to step 9:
The number 97 fits into 420 4 times, leaving a remainder of 32.
The number 4 becomes the next digit in our result. 
Result so far: 136.8144
Subtract 388 from 420 to get 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

The final result is 136.8144 with a remainder of 0.00032.