Let's divide 6683738 by 511
We want to figure out the number of times 6683738 can be divided by 511.

Moving on to step 1:
511 can be fit into 6 0 times, resulting in a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 6 after subtracting 0 from 6.
Include the next digit (6) from the dividend after 6, then repeat: 66 / 511

Going ahead to step 2:
When dividing 66 by 511, we get 0 with a remainder of 66.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 66, we end up with 66.
Take the next digit (8) from the dividend and append it to 66, then repeat: 668 / 511

Let's proceed to step 3:
If we divide 668 by 511, we get 1 and a remainder of 157.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Deduct 511 from 668 and we're left with 157.
Append the next digit (3) from the dividend to 157 and continue with: 1573 / 511

Let's proceed to step 4:
The number 511 fits into 1573 3 times, leaving a remainder of 40.
Put 3 as the next digit of the answer. 
Result so far: 13.0
Deduct 1533 from 1573 and we're left with 40.
Bring next digit (7) of the dividend behind the 40 and repeat the process: 407 / 511

Advancing to step 5:
511 goes into 407 0 times with a remainder of 407.
Put 0 as the next digit of the answer. 
Result so far: 130.0
If we take 0 away from 407, we end up with 407.
Take the next digit (3) from the dividend and append it to 407, then repeat: 4073 / 511

Let's proceed to step 6:
511 goes into 4073 7 times with a remainder of 496.
The next digit of our result is 7. 
Result so far: 1307.0
If we subtract 3577 from 4073, we get 496.
Fetch the next digit (8) from the dividend, attach it to 496 and continue: 4968 / 511

Advancing to step 7:
4968 divided by 511 is 9 with a remainder of 369.
Use 9 as the next digit of our solution. 
Result so far: 13079.0
The remainder is 369 after subtracting 4599 from 4968.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3690, and continue the process.

Step 8:
3690 divided by 511 is 7 with a remainder of 113.
Record the quotient 7 as the next digit in the result. 
Result so far: 13079.7
Deduct 3577 from 3690 and we're left with 113.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1130, and continue the process.

On to step 9:
If we divide 1130 by 511, we get 2 and a remainder of 108.
The next digit of our result is 2. 
Result so far: 13079.72
The remainder is 108 after subtracting 1022 from 1130.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1080, and continue the process.

Going ahead to step 10:
511 can be fit into 1080 2 times, resulting in a remainder of 58.
The next digit of our result is 2. 
Result so far: 13079.722
Subtract 1022 from 1080 to get 58.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

In conclusion, the division gives 13079.722 with a balance of 0.0058.