We're dividing 966413 by 271 
We want to figure out the number of times 966413 can be divided by 271.

Step 1:
271 goes into 9 0 times with a remainder of 9.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 9 and we're left with 9.
Grab the next digit (6) from the dividend, add it to 9, then carry on: 96 / 271

Let's proceed to step 2:
96 divided by 271 is 0 with a remainder of 96.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 96, we get 96.
Grab the next digit (6) from the dividend, add it to 96, then carry on: 966 / 271

Going ahead to step 3:
When dividing 966 by 271, we get 3 with a remainder of 153.
Write down 3 as next digit of the result. 
Result so far: 3.0
If we take 813 away from 966, we end up with 153.
Take the next digit (4) from the dividend and append it to 153, then repeat: 1534 / 271

Let's proceed to step 4:
The number 271 fits into 1534 5 times, leaving a remainder of 179.
Put 5 as the next digit of the answer. 
Result so far: 35.0
Subtract 1355 from 1534 to get 179.
Append the next digit (1) from the dividend to 179 and continue with: 1791 / 271

Step 5:
271 goes into 1791 6 times with a remainder of 165.
The number 6 becomes the next digit in our result. 
Result so far: 356.0
Deduct 1626 from 1791 and we're left with 165.
Take the next digit (3) from the dividend and append it to 165, then repeat: 1653 / 271

Moving on to step 6:
If we divide 1653 by 271, we get 6 and a remainder of 27.
Use 6 as the next digit of our solution. 
Result so far: 3566.0
The remainder is 27 after subtracting 1626 from 1653.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Advancing to step 7:
271 goes into 270 0 times with a remainder of 270.
Write down 0 as next digit of the result. 
Result so far: 3566.0
If we take 0 away from 270, we end up with 270.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2700, and continue the process.

Going ahead to step 8:
If we divide 2700 by 271, we get 9 and a remainder of 261.
Put 9 as the next digit of the answer. 
Result so far: 3566.09
The remainder is 261 after subtracting 2439 from 2700.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2610, and continue the process.

Let's proceed to step 9:
The number 271 fits into 2610 9 times, leaving a remainder of 171.
Use 9 as the next digit of our solution. 
Result so far: 3566.099
If we take 2439 away from 2610, we end up with 171.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1710, and continue the process.

In conclusion, the division gives 3566.099 with a balance of 0.0171.