966631 ÷ 44 
We want to divide 966631 by 44.

On to step 1:
When dividing 9 by 44, we get 0 with a remainder of 9.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 9 and we're left with 9.
Include the next digit (6) from the dividend after 9, then repeat: 96 / 44

On to step 2:
44 goes into 96 2 times with a remainder of 8.
Use 2 as the next digit of our solution. 
Result so far: 2.0
Subtracting 88 from 96 leaves us with 8.
Take the next digit (6) from the dividend and append it to 8, then repeat: 86 / 44

Let's proceed to step 3:
44 can be fit into 86 1 times, resulting in a remainder of 42.
The number 1 becomes the next digit in our result. 
Result so far: 21.0
Deduct 44 from 86 and we're left with 42.
Take the next digit (6) from the dividend and append it to 42, then repeat: 426 / 44

Advancing to step 4:
The number 44 fits into 426 9 times, leaving a remainder of 30.
Use 9 as the next digit of our solution. 
Result so far: 219.0
If we subtract 396 from 426, we get 30.
Append the next digit (3) from the dividend to 30 and continue with: 303 / 44

Let's proceed to step 5:
44 can be fit into 303 6 times, resulting in a remainder of 39.
Write down 6 as next digit of the result. 
Result so far: 2196.0
Subtract 264 from 303 to get 39.
Append the next digit (1) from the dividend to 39 and continue with: 391 / 44

Going ahead to step 6:
When dividing 391 by 44, we get 8 with a remainder of 39.
Use 8 as the next digit of our solution. 
Result so far: 21968.0
Deduct 352 from 391 and we're left with 39.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

Moving on to step 7:
390 divided by 44 is 8 with a remainder of 38.
Record the quotient 8 as the next digit in the result. 
Result so far: 21968.8
If we subtract 352 from 390, we get 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Step 8:
44 goes into 380 8 times with a remainder of 28.
The number 8 becomes the next digit in our result. 
Result so far: 21968.88
Subtract 352 from 380 to get 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

The final outcome is 21968.88, with a leftover of 0.028.