We look at the division of 414338 by 44 
We're looking to find how many times 44 goes into 414338.

On to step 1:
44 goes into 4 0 times with a remainder of 4.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 4, we get 4.
Take the next digit (1) from the dividend and append it to 4, then repeat: 41 / 44

Advancing to step 2:
44 goes into 41 0 times with a remainder of 41.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 41, we get 41.
Take the next digit (4) from the dividend and append it to 41, then repeat: 414 / 44

Advancing to step 3:
414 divided by 44 is 9 with a remainder of 18.
Write down 9 as next digit of the result. 
Result so far: 9.0
If we take 396 away from 414, we end up with 18.
Bring next digit (3) of the dividend behind the 18 and repeat the process: 183 / 44

Step 4:
If we divide 183 by 44, we get 4 and a remainder of 7.
The next digit of our result is 4. 
Result so far: 94.0
Deduct 176 from 183 and we're left with 7.
Bring next digit (3) of the dividend behind the 7 and repeat the process: 73 / 44

Going ahead to step 5:
44 goes into 73 1 times with a remainder of 29.
The number 1 becomes the next digit in our result. 
Result so far: 941.0
If we take 44 away from 73, we end up with 29.
Append the next digit (8) from the dividend to 29 and continue with: 298 / 44

Moving on to step 6:
44 can be fit into 298 6 times, resulting in a remainder of 34.
The next digit of our result is 6. 
Result so far: 9416.0
If we subtract 264 from 298, we get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Step 7:
44 can be fit into 340 7 times, resulting in a remainder of 32.
Write down 7 as next digit of the result. 
Result so far: 9416.7
If we subtract 308 from 340, we 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.

Let's proceed to step 8:
The number 44 fits into 320 7 times, leaving a remainder of 12.
Put 7 as the next digit of the answer. 
Result so far: 9416.77
If we take 308 away from 320, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

In conclusion, the division gives 9416.77 with a balance of 0.012.