We're dividing 577515 by 9 
We're looking to find how many times 9 goes into 577515.

Going ahead to step 1:
9 goes into 5 0 times with a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Append the next digit (7) from the dividend to 5 and continue with: 57 / 9

Advancing to step 2:
57 divided by 9 is 6 with a remainder of 3.
Put 6 as the next digit of the answer. 
Result so far: 6.0
If we subtract 54 from 57, we get 3.
Append the next digit (7) from the dividend to 3 and continue with: 37 / 9

On to step 3:
37 divided by 9 is 4 with a remainder of 1.
Use 4 as the next digit of our solution. 
Result so far: 64.0
Subtracting 36 from 37 leaves us with 1.
Append the next digit (5) from the dividend to 1 and continue with: 15 / 9

Moving on to step 4:
15 divided by 9 is 1 with a remainder of 6.
The next digit of our result is 1. 
Result so far: 641.0
Subtract 9 from 15 to get 6.
Bring next digit (1) of the dividend behind the 6 and repeat the process: 61 / 9

Moving on to step 5:
9 can be fit into 61 6 times, resulting in a remainder of 7.
Use 6 as the next digit of our solution. 
Result so far: 6416.0
Deduct 54 from 61 and we're left with 7.
Grab the next digit (5) from the dividend, add it to 7, then carry on: 75 / 9

Advancing to step 6:
75 divided by 9 is 8 with a remainder of 3.
The number 8 becomes the next digit in our result. 
Result so far: 64168.0
Subtracting 72 from 75 leaves us with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

On to step 7:
The number 9 fits into 30 3 times, leaving a remainder of 3.
The next digit of our result is 3. 
Result so far: 64168.3
Subtracting 27 from 30 leaves us with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Advancing to step 8:
The number 9 fits into 30 3 times, leaving a remainder of 3.
Record the quotient 3 as the next digit in the result. 
Result so far: 64168.33
Deduct 27 from 30 and we're left with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

In conclusion, the division gives 64168.33 with a balance of 0.003.