We look at the division of 513199 by 9 
Our goal is to divide 513199 by 9.

Step 1:
9 can be fit into 5 0 times, resulting in a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Include the next digit (1) from the dividend after 5, then repeat: 51 / 9

Step 2:
When dividing 51 by 9, we get 5 with a remainder of 6.
Record the quotient 5 as the next digit in the result. 
Result so far: 5.0
Deduct 45 from 51 and we're left with 6.
Fetch the next digit (3) from the dividend, attach it to 6 and continue: 63 / 9

Advancing to step 3:
9 can be fit into 63 7 times, resulting in a remainder of 0.
Record the quotient 7 as the next digit in the result. 
Result so far: 57.0
If we subtract 63 from 63, we get 0.
Include the next digit (1) from the dividend after 0, then repeat: 1 / 9

Step 4:
The number 9 fits into 1 0 times, leaving a remainder of 1.
The next digit of our result is 0. 
Result so far: 570.0
If we subtract 0 from 1, we get 1.
Grab the next digit (9) from the dividend, add it to 1, then carry on: 19 / 9

Let's proceed to step 5:
The number 9 fits into 19 2 times, leaving a remainder of 1.
Put 2 as the next digit of the answer. 
Result so far: 5702.0
Deduct 18 from 19 and we're left with 1.
Fetch the next digit (9) from the dividend, attach it to 1 and continue: 19 / 9

Advancing to step 6:
When dividing 19 by 9, we get 2 with a remainder of 1.
Write down 2 as next digit of the result. 
Result so far: 57022.0
Subtract 18 from 19 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Let's proceed to step 7:
9 goes into 10 1 times with a remainder of 1.
Use 1 as the next digit of our solution. 
Result so far: 57022.1
Subtract 9 from 10 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 8:
10 divided by 9 is 1 with a remainder of 1.
Write down 1 as next digit of the result. 
Result so far: 57022.11
If we subtract 9 from 10, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

In conclusion, the division gives 57022.11 with a balance of 0.001.