510825 divided by 82 
Our goal is to divide 510825 by 82.

Moving on to step 1:
The number 82 fits into 5 0 times, leaving a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Include the next digit (1) from the dividend after 5, then repeat: 51 / 82

Moving on to step 2:
82 goes into 51 0 times with a remainder of 51.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 51 to get 51.
Include the next digit (0) from the dividend after 51, then repeat: 510 / 82

Going ahead to step 3:
The number 82 fits into 510 6 times, leaving a remainder of 18.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
Subtract 492 from 510 to get 18.
Take the next digit (8) from the dividend and append it to 18, then repeat: 188 / 82

Advancing to step 4:
If we divide 188 by 82, we get 2 and a remainder of 24.
Write down 2 as next digit of the result. 
Result so far: 62.0
If we subtract 164 from 188, we get 24.
Append the next digit (2) from the dividend to 24 and continue with: 242 / 82

Step 5:
82 goes into 242 2 times with a remainder of 78.
Put 2 as the next digit of the answer. 
Result so far: 622.0
Deduct 164 from 242 and we're left with 78.
Append the next digit (5) from the dividend to 78 and continue with: 785 / 82

Step 6:
82 can be fit into 785 9 times, resulting in a remainder of 47.
Write down 9 as next digit of the result. 
Result so far: 6229.0
Deduct 738 from 785 and we're left with 47.
Since there are no more digits in the dividend, we add a zero to the remainder making it 470, and continue the process.

Step 7:
470 divided by 82 is 5 with a remainder of 60.
Use 5 as the next digit of our solution. 
Result so far: 6229.5
Subtracting 410 from 470 leaves us with 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Let's proceed to step 8:
If we divide 600 by 82, we get 7 and a remainder of 26.
The number 7 becomes the next digit in our result. 
Result so far: 6229.57
Deduct 574 from 600 and we're left with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

On to step 9:
When dividing 260 by 82, we get 3 with a remainder of 14.
Use 3 as the next digit of our solution. 
Result so far: 6229.573
The remainder is 14 after subtracting 246 from 260.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Moving on to step 10:
The number 82 fits into 140 1 times, leaving a remainder of 58.
The next digit of our result is 1. 
Result so far: 6229.5731
If we take 82 away from 140, we end up with 58.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

Moving on to step 11:
The number 82 fits into 580 7 times, leaving a remainder of 6.
The next digit of our result is 7. 
Result so far: 6229.57317
Subtract 574 from 580 to get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

On to step 12:
When dividing 60 by 82, we get 0 with a remainder of 60.
The next digit of our result is 0. 
Result so far: 6229.57317
If we subtract 0 from 60, we get 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

On to step 13:
If we divide 600 by 82, we get 7 and a remainder of 26.
Write down 7 as next digit of the result. 
Result so far: 6229.5731707
Deduct 574 from 600 and we're left with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Advancing to step 14:
82 goes into 260 3 times with a remainder of 14.
Write down 3 as next digit of the result. 
Result so far: 6229.57317073
Subtract 246 from 260 to get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

In conclusion, the division gives 6229.57317073 with a balance of 1.4e-08.