We're dividing 568261 by 9 
We want to figure out the number of times 568261 can be divided by 9.

On to step 1:
5 divided by 9 is 0 with a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Append the next digit (6) from the dividend to 5 and continue with: 56 / 9

Let's proceed to step 2:
When dividing 56 by 9, we get 6 with a remainder of 2.
Use 6 as the next digit of our solution. 
Result so far: 6.0
Subtract 54 from 56 to get 2.
Take the next digit (8) from the dividend and append it to 2, then repeat: 28 / 9

Let's proceed to step 3:
If we divide 28 by 9, we get 3 and a remainder of 1.
Use 3 as the next digit of our solution. 
Result so far: 63.0
Subtracting 27 from 28 leaves us with 1.
Grab the next digit (2) from the dividend, add it to 1, then carry on: 12 / 9

On to step 4:
When dividing 12 by 9, we get 1 with a remainder of 3.
The number 1 becomes the next digit in our result. 
Result so far: 631.0
The remainder is 3 after subtracting 9 from 12.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 9

Let's proceed to step 5:
When dividing 36 by 9, we get 4 with a remainder of 0.
Use 4 as the next digit of our solution. 
Result so far: 6314.0
Subtract 36 from 36 to get 0.
Bring next digit (1) of the dividend behind the 0 and repeat the process: 1 / 9

Advancing to step 6:
1 divided by 9 is 0 with a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 63140.0
Subtracting 0 from 1 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.

On to step 7:
9 can be fit into 10 1 times, resulting in a remainder of 1.
The next digit of our result is 1. 
Result so far: 63140.1
If we subtract 9 from 10, we 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.

Step 8:
When dividing 10 by 9, we get 1 with a remainder of 1.
Put 1 as the next digit of the answer. 
Result so far: 63140.11
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.

After the division, we end up with 63140.11 and a remainder of 0.001.