We look at the division of 820129 by 9 
We're looking to find how many times 9 goes into 820129.

Let's proceed to step 1:
When dividing 8 by 9, we get 0 with 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.
Fetch the next digit (2) from the dividend, attach it to 8 and continue: 82 / 9

Advancing to step 2:
82 divided by 9 is 9 with a remainder of 1.
Put 9 as the next digit of the answer. 
Result so far: 9.0
Subtract 81 from 82 to get 1.
Fetch the next digit (0) from the dividend, attach it to 1 and continue: 10 / 9

Moving on to step 3:
9 can be fit into 10 1 times, resulting in a remainder of 1.
Write down 1 as next digit of the result. 
Result so far: 91.0
If we take 9 away from 10, we end up with 1.
Include the next digit (1) from the dividend after 1, then repeat: 11 / 9

Going ahead to step 4:
11 divided by 9 is 1 with a remainder of 2.
Use 1 as the next digit of our solution. 
Result so far: 911.0
The remainder is 2 after subtracting 9 from 11.
Fetch the next digit (2) from the dividend, attach it to 2 and continue: 22 / 9

Advancing to step 5:
The number 9 fits into 22 2 times, leaving a remainder of 4.
Put 2 as the next digit of the answer. 
Result so far: 9112.0
Subtracting 18 from 22 leaves us with 4.
Include the next digit (9) from the dividend after 4, then repeat: 49 / 9

Going ahead to step 6:
9 goes into 49 5 times with a remainder of 4.
Put 5 as the next digit of the answer. 
Result so far: 91125.0
Deduct 45 from 49 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Let's proceed to step 7:
9 can be fit into 40 4 times, resulting in a remainder of 4.
The next digit of our result is 4. 
Result so far: 91125.4
If we subtract 36 from 40, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 8:
9 can be fit into 40 4 times, resulting in a remainder of 4.
Record the quotient 4 as the next digit in the result. 
Result so far: 91125.44
Deduct 36 from 40 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

The final outcome is 91125.44, with a leftover of 0.004.