We look at the division of 129813 by 9 
We're looking to find how many times 9 goes into 129813.

Moving on to step 1:
The number 9 fits into 1 0 times, leaving a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Take the next digit (2) from the dividend and append it to 1, then repeat: 12 / 9

Moving on to step 2:
If we divide 12 by 9, we get 1 and a remainder of 3.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtract 9 from 12 to get 3.
Append the next digit (9) from the dividend to 3 and continue with: 39 / 9

Advancing to step 3:
When dividing 39 by 9, we get 4 with a remainder of 3.
Write down 4 as next digit of the result. 
Result so far: 14.0
If we take 36 away from 39, we end up with 3.
Fetch the next digit (8) from the dividend, attach it to 3 and continue: 38 / 9

Advancing to step 4:
The number 9 fits into 38 4 times, leaving a remainder of 2.
The next digit of our result is 4. 
Result so far: 144.0
Deduct 36 from 38 and we're left with 2.
Fetch the next digit (1) from the dividend, attach it to 2 and continue: 21 / 9

Step 5:
9 can be fit into 21 2 times, resulting in a remainder of 3.
Put 2 as the next digit of the answer. 
Result so far: 1442.0
Subtract 18 from 21 to get 3.
Append the next digit (3) from the dividend to 3 and continue with: 33 / 9

Moving on to step 6:
The number 9 fits into 33 3 times, leaving a remainder of 6.
The next digit of our result is 3. 
Result so far: 14423.0
Deduct 27 from 33 and we're left with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Let's proceed to step 7:
The number 9 fits into 60 6 times, leaving a remainder of 6.
The number 6 becomes the next digit in our result. 
Result so far: 14423.6
The remainder is 6 after subtracting 54 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Going ahead to step 8:
9 can be fit into 60 6 times, resulting in a remainder of 6.
Write down 6 as next digit of the result. 
Result so far: 14423.66
Deduct 54 from 60 and we're left with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

The final outcome is 14423.66, with a leftover of 0.006.