We look at the division of 563564 by 9 
We're looking to find how many times 9 goes into 563564.

Let's proceed to step 1:
When dividing 5 by 9, we get 0 with a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Append the next digit (6) from the dividend to 5 and continue with: 56 / 9

Advancing to step 2:
9 can be fit into 56 6 times, resulting in a remainder of 2.
The next digit of our result is 6. 
Result so far: 6.0
If we take 54 away from 56, we end up with 2.
Take the next digit (3) from the dividend and append it to 2, then repeat: 23 / 9

Let's proceed to step 3:
9 can be fit into 23 2 times, resulting in a remainder of 5.
Record the quotient 2 as the next digit in the result. 
Result so far: 62.0
If we take 18 away from 23, we end up with 5.
Bring next digit (5) of the dividend behind the 5 and repeat the process: 55 / 9

Step 4:
The number 9 fits into 55 6 times, leaving a remainder of 1.
Record the quotient 6 as the next digit in the result. 
Result so far: 626.0
Subtracting 54 from 55 leaves us with 1.
Take the next digit (6) from the dividend and append it to 1, then repeat: 16 / 9

Going ahead to step 5:
If we divide 16 by 9, we get 1 and a remainder of 7.
The number 1 becomes the next digit in our result. 
Result so far: 6261.0
Subtract 9 from 16 to get 7.
Bring next digit (4) of the dividend behind the 7 and repeat the process: 74 / 9

On to step 6:
74 divided by 9 is 8 with a remainder of 2.
Record the quotient 8 as the next digit in the result. 
Result so far: 62618.0
If we take 72 away from 74, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 7:
The number 9 fits into 20 2 times, leaving a remainder of 2.
Write down 2 as next digit of the result. 
Result so far: 62618.2
If we take 18 away from 20, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 8:
If we divide 20 by 9, we get 2 and a remainder of 2.
Record the quotient 2 as the next digit in the result. 
Result so far: 62618.22
Deduct 18 from 20 and we're left with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

The final result is 62618.22 with a remainder of 0.002.