We look at the division of 30565 by 9 
We want to divide 30565 by 9.

Going ahead to step 1:
9 goes into 3 0 times with a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 3 to get 3.
Grab the next digit (0) from the dividend, add it to 3, then carry on: 30 / 9

Step 2:
9 goes into 30 3 times with a remainder of 3.
Use 3 as the next digit of our solution. 
Result so far: 3.0
The remainder is 3 after subtracting 27 from 30.
Bring next digit (5) of the dividend behind the 3 and repeat the process: 35 / 9

Step 3:
When dividing 35 by 9, we get 3 with a remainder of 8.
Record the quotient 3 as the next digit in the result. 
Result so far: 33.0
If we subtract 27 from 35, we get 8.
Include the next digit (6) from the dividend after 8, then repeat: 86 / 9

Moving on to step 4:
The number 9 fits into 86 9 times, leaving a remainder of 5.
Write down 9 as next digit of the result. 
Result so far: 339.0
If we take 81 away from 86, we end up with 5.
Append the next digit (5) from the dividend to 5 and continue with: 55 / 9

Going ahead to step 5:
9 goes into 55 6 times with a remainder of 1.
The number 6 becomes the next digit in our result. 
Result so far: 3396.0
Deduct 54 from 55 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Advancing to step 6:
When dividing 10 by 9, we get 1 with a remainder of 1.
Record the quotient 1 as the next digit in the result. 
Result so far: 3396.1
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.

Moving on to step 7:
10 divided by 9 is 1 with a remainder of 1.
The next digit of our result is 1. 
Result so far: 3396.11
Subtracting 9 from 10 leaves us with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

The final result is 3396.11 with a remainder of 0.001.