563034 ÷ 9 
We want to figure out the number of times 563034 can be divided by 9.

On to step 1:
If we divide 5 by 9, we get 0 and a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Grab the next digit (6) from the dividend, add it to 5, then carry on: 56 / 9

Step 2:
If we divide 56 by 9, we get 6 and a remainder of 2.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
If we subtract 54 from 56, we get 2.
Append the next digit (3) from the dividend to 2 and continue with: 23 / 9

On to step 3:
9 goes into 23 2 times with a remainder of 5.
Use 2 as the next digit of our solution. 
Result so far: 62.0
If we subtract 18 from 23, we get 5.
Take the next digit (0) from the dividend and append it to 5, then repeat: 50 / 9

Let's proceed to step 4:
The number 9 fits into 50 5 times, leaving a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 625.0
Subtracting 45 from 50 leaves us with 5.
Take the next digit (3) from the dividend and append it to 5, then repeat: 53 / 9

Advancing to step 5:
The number 9 fits into 53 5 times, leaving a remainder of 8.
Use 5 as the next digit of our solution. 
Result so far: 6255.0
If we subtract 45 from 53, we get 8.
Append the next digit (4) from the dividend to 8 and continue with: 84 / 9

Step 6:
If we divide 84 by 9, we get 9 and a remainder of 3.
Record the quotient 9 as the next digit in the result. 
Result so far: 62559.0
Subtracting 81 from 84 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.

Let's proceed to step 7:
30 divided by 9 is 3 with a remainder of 3.
Use 3 as the next digit of our solution. 
Result so far: 62559.3
If we subtract 27 from 30, we get 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 8:
The number 9 fits into 30 3 times, leaving a remainder of 3.
The number 3 becomes the next digit in our result. 
Result so far: 62559.33
The remainder is 3 after subtracting 27 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

The quotient of the division is 62559.33, and the remainder is 0.003.