We look at the division of 509575 by 9 
We want to divide 509575 by 9.

Let's proceed to step 1:
If we divide 5 by 9, we get 0 and a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Include the next digit (0) from the dividend after 5, then repeat: 50 / 9

Let's proceed to step 2:
If we divide 50 by 9, we get 5 and a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 5.0
If we take 45 away from 50, we end up with 5.
Append the next digit (9) from the dividend to 5 and continue with: 59 / 9

Let's proceed to step 3:
9 goes into 59 6 times with a remainder of 5.
Record the quotient 6 as the next digit in the result. 
Result so far: 56.0
Deduct 54 from 59 and we're left with 5.
Take the next digit (5) from the dividend and append it to 5, then repeat: 55 / 9

Going ahead to step 4:
55 divided by 9 is 6 with a remainder of 1.
Write down 6 as next digit of the result. 
Result so far: 566.0
If we subtract 54 from 55, we get 1.
Take the next digit (7) from the dividend and append it to 1, then repeat: 17 / 9

Moving on to step 5:
9 goes into 17 1 times with a remainder of 8.
The number 1 becomes the next digit in our result. 
Result so far: 5661.0
If we subtract 9 from 17, we get 8.
Grab the next digit (5) from the dividend, add it to 8, then carry on: 85 / 9

Moving on to step 6:
The number 9 fits into 85 9 times, leaving a remainder of 4.
Use 9 as the next digit of our solution. 
Result so far: 56619.0
The remainder is 4 after subtracting 81 from 85.
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:
If we divide 40 by 9, we get 4 and a remainder of 4.
The next digit of our result is 4. 
Result so far: 56619.4
Subtract 36 from 40 to 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.

Let's proceed to step 8:
The number 9 fits into 40 4 times, leaving a remainder of 4.
Use 4 as the next digit of our solution. 
Result so far: 56619.44
Subtracting 36 from 40 leaves us 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.

In conclusion, the division gives 56619.44 with a balance of 0.004.