We're dividing 9619 by 71 
We're looking to find how many times 71 goes into 9619.

Step 1:
71 can be fit into 9 0 times, resulting in a remainder of 9.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 9 after subtracting 0 from 9.
Include the next digit (6) from the dividend after 9, then repeat: 96 / 71

Moving on to step 2:
71 goes into 96 1 times with a remainder of 25.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Deduct 71 from 96 and we're left with 25.
Fetch the next digit (1) from the dividend, attach it to 25 and continue: 251 / 71

Let's proceed to step 3:
When dividing 251 by 71, we get 3 with a remainder of 38.
The number 3 becomes the next digit in our result. 
Result so far: 13.0
Subtract 213 from 251 to get 38.
Grab the next digit (9) from the dividend, add it to 38, then carry on: 389 / 71

Let's proceed to step 4:
71 can be fit into 389 5 times, resulting in a remainder of 34.
The next digit of our result is 5. 
Result so far: 135.0
Subtracting 355 from 389 leaves us with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

On to step 5:
340 divided by 71 is 4 with a remainder of 56.
Write down 4 as next digit of the result. 
Result so far: 135.4
Subtract 284 from 340 to get 56.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

Let's proceed to step 6:
If we divide 560 by 71, we get 7 and a remainder of 63.
Put 7 as the next digit of the answer. 
Result so far: 135.47
If we subtract 497 from 560, we get 63.
Since there are no more digits in the dividend, we add a zero to the remainder making it 630, and continue the process.

Going ahead to step 7:
71 can be fit into 630 8 times, resulting in a remainder of 62.
Put 8 as the next digit of the answer. 
Result so far: 135.478
The remainder is 62 after subtracting 568 from 630.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

On to step 8:
The number 71 fits into 620 8 times, leaving a remainder of 52.
The number 8 becomes the next digit in our result. 
Result so far: 135.4788
The remainder is 52 after subtracting 568 from 620.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

In conclusion, the division gives 135.4788 with a balance of 0.00052.