55575969 ÷ 966 
Our goal is to divide 55575969 by 966.

Step 1:
966 can be fit into 5 0 times, resulting in a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Include the next digit (5) from the dividend after 5, then repeat: 55 / 966

Let's proceed to step 2:
When dividing 55 by 966, we get 0 with a remainder of 55.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 55, we get 55.
Take the next digit (5) from the dividend and append it to 55, then repeat: 555 / 966

Moving on to step 3:
966 can be fit into 555 0 times, resulting in a remainder of 555.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 555, we get 555.
Grab the next digit (7) from the dividend, add it to 555, then carry on: 5557 / 966

Advancing to step 4:
When dividing 5557 by 966, we get 5 with a remainder of 727.
Use 5 as the next digit of our solution. 
Result so far: 5.0
The remainder is 727 after subtracting 4830 from 5557.
Include the next digit (5) from the dividend after 727, then repeat: 7275 / 966

On to step 5:
When dividing 7275 by 966, we get 7 with a remainder of 513.
Use 7 as the next digit of our solution. 
Result so far: 57.0
If we subtract 6762 from 7275, we get 513.
Append the next digit (9) from the dividend to 513 and continue with: 5139 / 966

On to step 6:
966 goes into 5139 5 times with a remainder of 309.
Record the quotient 5 as the next digit in the result. 
Result so far: 575.0
The remainder is 309 after subtracting 4830 from 5139.
Fetch the next digit (6) from the dividend, attach it to 309 and continue: 3096 / 966

Going ahead to step 7:
966 goes into 3096 3 times with a remainder of 198.
The next digit of our result is 3. 
Result so far: 5753.0
If we take 2898 away from 3096, we end up with 198.
Take the next digit (9) from the dividend and append it to 198, then repeat: 1989 / 966

Step 8:
966 can be fit into 1989 2 times, resulting in a remainder of 57.
The next digit of our result is 2. 
Result so far: 57532.0
If we take 1932 away from 1989, we end up with 57.
Since there are no more digits in the dividend, we add a zero to the remainder making it 570, and continue the process.

On to step 9:
570 divided by 966 is 0 with a remainder of 570.
The number 0 becomes the next digit in our result. 
Result so far: 57532.0
The remainder is 570 after subtracting 0 from 570.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5700, and continue the process.

Let's proceed to step 10:
966 goes into 5700 5 times with a remainder of 870.
Write down 5 as next digit of the result. 
Result so far: 57532.05
If we subtract 4830 from 5700, we get 870.
Since there are no more digits in the dividend, we add a zero to the remainder making it 8700, and continue the process.

Advancing to step 11:
When dividing 8700 by 966, we get 9 with a remainder of 6.
Put 9 as the next digit of the answer. 
Result so far: 57532.059
Deduct 8694 from 8700 and we're left with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Advancing to step 12:
When dividing 60 by 966, we get 0 with a remainder of 60.
The number 0 becomes the next digit in our result. 
Result so far: 57532.059
The remainder is 60 after subtracting 0 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Going ahead to step 13:
600 divided by 966 is 0 with a remainder of 600.
Record the quotient 0 as the next digit in the result. 
Result so far: 57532.059
Subtracting 0 from 600 leaves us with 600.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6000, and continue the process.

In conclusion, the division gives 57532.059 with a balance of 0.0006.