871003 ÷ 44 
Our goal is to divide 871003 by 44.

Advancing to step 1:
If we divide 8 by 44, we get 0 and a remainder of 8.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 8 leaves us with 8.
Bring next digit (7) of the dividend behind the 8 and repeat the process: 87 / 44

Step 2:
44 can be fit into 87 1 times, resulting in a remainder of 43.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we subtract 44 from 87, we get 43.
Append the next digit (1) from the dividend to 43 and continue with: 431 / 44

Step 3:
44 can be fit into 431 9 times, resulting in a remainder of 35.
The number 9 becomes the next digit in our result. 
Result so far: 19.0
Subtract 396 from 431 to get 35.
Bring next digit (0) of the dividend behind the 35 and repeat the process: 350 / 44

Advancing to step 4:
350 divided by 44 is 7 with a remainder of 42.
Put 7 as the next digit of the answer. 
Result so far: 197.0
If we take 308 away from 350, we end up with 42.
Grab the next digit (0) from the dividend, add it to 42, then carry on: 420 / 44

Moving on to step 5:
The number 44 fits into 420 9 times, leaving a remainder of 24.
Write down 9 as next digit of the result. 
Result so far: 1979.0
Subtract 396 from 420 to get 24.
Grab the next digit (3) from the dividend, add it to 24, then carry on: 243 / 44

Advancing to step 6:
44 goes into 243 5 times with a remainder of 23.
Use 5 as the next digit of our solution. 
Result so far: 19795.0
If we subtract 220 from 243, we get 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Let's proceed to step 7:
44 goes into 230 5 times with a remainder of 10.
Record the quotient 5 as the next digit in the result. 
Result so far: 19795.5
Deduct 220 from 230 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 8:
If we divide 100 by 44, we get 2 and a remainder of 12.
Use 2 as the next digit of our solution. 
Result so far: 19795.52
If we take 88 away from 100, 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.

On to step 9:
If we divide 120 by 44, we get 2 and a remainder of 32.
Write down 2 as next digit of the result. 
Result so far: 19795.522
Deduct 88 from 120 and we're left with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

The final outcome is 19795.522, with a leftover of 0.0032.