We look at the division of 557237 by 641 
We want to divide 557237 by 641.

Moving on to step 1:
641 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
Subtracting 0 from 5 leaves us with 5.
Append the next digit (5) from the dividend to 5 and continue with: 55 / 641

Advancing to step 2:
641 goes into 55 0 times with a remainder of 55.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 55 leaves us with 55.
Bring next digit (7) of the dividend behind the 55 and repeat the process: 557 / 641

Going ahead to step 3:
641 can be fit into 557 0 times, resulting in a remainder of 557.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 557 leaves us with 557.
Take the next digit (2) from the dividend and append it to 557, then repeat: 5572 / 641

Going ahead to step 4:
The number 641 fits into 5572 8 times, leaving a remainder of 444.
The next digit of our result is 8. 
Result so far: 8.0
If we subtract 5128 from 5572, we get 444.
Take the next digit (3) from the dividend and append it to 444, then repeat: 4443 / 641

Advancing to step 5:
641 goes into 4443 6 times with a remainder of 597.
Record the quotient 6 as the next digit in the result. 
Result so far: 86.0
If we take 3846 away from 4443, we end up with 597.
Fetch the next digit (7) from the dividend, attach it to 597 and continue: 5977 / 641

Let's proceed to step 6:
5977 divided by 641 is 9 with a remainder of 208.
Write down 9 as next digit of the result. 
Result so far: 869.0
Subtracting 5769 from 5977 leaves us with 208.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2080, and continue the process.

Let's proceed to step 7:
641 goes into 2080 3 times with a remainder of 157.
Put 3 as the next digit of the answer. 
Result so far: 869.3
Subtracting 1923 from 2080 leaves us with 157.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1570, and continue the process.

Advancing to step 8:
641 goes into 1570 2 times with a remainder of 288.
The next digit of our result is 2. 
Result so far: 869.32
Subtract 1282 from 1570 to get 288.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2880, and continue the process.

Let's proceed to step 9:
2880 divided by 641 is 4 with a remainder of 316.
Write down 4 as next digit of the result. 
Result so far: 869.324
Deduct 2564 from 2880 and we're left with 316.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3160, and continue the process.

On to step 10:
The number 641 fits into 3160 4 times, leaving a remainder of 596.
The next digit of our result is 4. 
Result so far: 869.3244
Subtracting 2564 from 3160 leaves us with 596.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5960, and continue the process.

After the division, we end up with 869.3244 and a remainder of 0.00596.