We're dividing 644050 by 824 
Our goal is to divide 644050 by 824.

Advancing to step 1:
When dividing 6 by 824, we get 0 with a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 6, we get 6.
Append the next digit (4) from the dividend to 6 and continue with: 64 / 824

Moving on to step 2:
The number 824 fits into 64 0 times, leaving a remainder of 64.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 64, we get 64.
Bring next digit (4) of the dividend behind the 64 and repeat the process: 644 / 824

Step 3:
824 can be fit into 644 0 times, resulting in a remainder of 644.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 644, we get 644.
Fetch the next digit (0) from the dividend, attach it to 644 and continue: 6440 / 824

Going ahead to step 4:
When dividing 6440 by 824, we get 7 with a remainder of 672.
Write down 7 as next digit of the result. 
Result so far: 7.0
If we subtract 5768 from 6440, we get 672.
Bring next digit (5) of the dividend behind the 672 and repeat the process: 6725 / 824

Going ahead to step 5:
6725 divided by 824 is 8 with a remainder of 133.
The next digit of our result is 8. 
Result so far: 78.0
Subtract 6592 from 6725 to get 133.
Take the next digit (0) from the dividend and append it to 133, then repeat: 1330 / 824

Advancing to step 6:
If we divide 1330 by 824, we get 1 and a remainder of 506.
Put 1 as the next digit of the answer. 
Result so far: 781.0
Deduct 824 from 1330 and we're left with 506.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5060, and continue the process.

Step 7:
The number 824 fits into 5060 6 times, leaving a remainder of 116.
Write down 6 as next digit of the result. 
Result so far: 781.6
Subtract 4944 from 5060 to get 116.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1160, and continue the process.

Let's proceed to step 8:
The number 824 fits into 1160 1 times, leaving a remainder of 336.
Use 1 as the next digit of our solution. 
Result so far: 781.61
If we take 824 away from 1160, we end up with 336.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3360, and continue the process.

Let's proceed to step 9:
The number 824 fits into 3360 4 times, leaving a remainder of 64.
Use 4 as the next digit of our solution. 
Result so far: 781.614
Deduct 3296 from 3360 and we're left with 64.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

Advancing to step 10:
When dividing 640 by 824, we get 0 with a remainder of 640.
Use 0 as the next digit of our solution. 
Result so far: 781.614
Subtracting 0 from 640 leaves us with 640.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6400, and continue the process.

Advancing to step 11:
824 goes into 6400 7 times with a remainder of 632.
The next digit of our result is 7. 
Result so far: 781.61407
Deduct 5768 from 6400 and we're left with 632.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6320, and continue the process.

Step 12:
The number 824 fits into 6320 7 times, leaving a remainder of 552.
Use 7 as the next digit of our solution. 
Result so far: 781.614077
The remainder is 552 after subtracting 5768 from 6320.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5520, and continue the process.

In conclusion, the division gives 781.614077 with a balance of 5.52e-05.