4438111 ÷ 553 
Our goal is to divide 4438111 by 553.

Advancing to step 1:
When dividing 4 by 553, we get 0 with a remainder of 4.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 4, we end up with 4.
Fetch the next digit (4) from the dividend, attach it to 4 and continue: 44 / 553

Moving on to step 2:
When dividing 44 by 553, we get 0 with a remainder of 44.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 44 leaves us with 44.
Append the next digit (3) from the dividend to 44 and continue with: 443 / 553

Step 3:
443 divided by 553 is 0 with a remainder of 443.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 443, we end up with 443.
Fetch the next digit (8) from the dividend, attach it to 443 and continue: 4438 / 553

Advancing to step 4:
553 goes into 4438 8 times with a remainder of 14.
Write down 8 as next digit of the result. 
Result so far: 8.0
If we subtract 4424 from 4438, we get 14.
Grab the next digit (1) from the dividend, add it to 14, then carry on: 141 / 553

Moving on to step 5:
If we divide 141 by 553, we get 0 and a remainder of 141.
The number 0 becomes the next digit in our result. 
Result so far: 80.0
If we subtract 0 from 141, we get 141.
Grab the next digit (1) from the dividend, add it to 141, then carry on: 1411 / 553

Moving on to step 6:
The number 553 fits into 1411 2 times, leaving a remainder of 305.
Put 2 as the next digit of the answer. 
Result so far: 802.0
Deduct 1106 from 1411 and we're left with 305.
Grab the next digit (1) from the dividend, add it to 305, then carry on: 3051 / 553

Step 7:
3051 divided by 553 is 5 with a remainder of 286.
Use 5 as the next digit of our solution. 
Result so far: 8025.0
Subtracting 2765 from 3051 leaves us with 286.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2860, and continue the process.

Going ahead to step 8:
553 goes into 2860 5 times with a remainder of 95.
Put 5 as the next digit of the answer. 
Result so far: 8025.5
The remainder is 95 after subtracting 2765 from 2860.
Since there are no more digits in the dividend, we add a zero to the remainder making it 950, and continue the process.

Step 9:
553 can be fit into 950 1 times, resulting in a remainder of 397.
Record the quotient 1 as the next digit in the result. 
Result so far: 8025.51
Deduct 553 from 950 and we're left with 397.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3970, and continue the process.

On to step 10:
When dividing 3970 by 553, we get 7 with a remainder of 99.
Use 7 as the next digit of our solution. 
Result so far: 8025.517
Deduct 3871 from 3970 and we're left with 99.
Since there are no more digits in the dividend, we add a zero to the remainder making it 990, and continue the process.

On to step 11:
The number 553 fits into 990 1 times, leaving a remainder of 437.
Write down 1 as next digit of the result. 
Result so far: 8025.5171
If we take 553 away from 990, we end up with 437.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4370, and continue the process.

Advancing to step 12:
The number 553 fits into 4370 7 times, leaving a remainder of 499.
Use 7 as the next digit of our solution. 
Result so far: 8025.51717
The remainder is 499 after subtracting 3871 from 4370.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4990, and continue the process.

Moving on to step 13:
553 goes into 4990 9 times with a remainder of 13.
Use 9 as the next digit of our solution. 
Result so far: 8025.517179
Subtracting 4977 from 4990 leaves us with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Advancing to step 14:
When dividing 130 by 553, we get 0 with a remainder of 130.
Record the quotient 0 as the next digit in the result. 
Result so far: 8025.517179
If we subtract 0 from 130, we get 130.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1300, and continue the process.

On to step 15:
553 can be fit into 1300 2 times, resulting in a remainder of 194.
The number 2 becomes the next digit in our result. 
Result so far: 8025.51717902
Subtract 1106 from 1300 to get 194.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1940, and continue the process.

After the division, we end up with 8025.51717902 and a remainder of 1.94e-07.