100566 ÷ 9 
We're looking to find how many times 9 goes into 100566.

On to step 1:
When dividing 1 by 9, we get 0 with a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 9

On to step 2:
9 can be fit into 10 1 times, resulting in a remainder of 1.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we subtract 9 from 10, we get 1.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 9

Let's proceed to step 3:
9 goes into 10 1 times with a remainder of 1.
The next digit of our result is 1. 
Result so far: 11.0
Subtracting 9 from 10 leaves us with 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 9

Let's proceed to step 4:
When dividing 15 by 9, we get 1 with a remainder of 6.
The number 1 becomes the next digit in our result. 
Result so far: 111.0
The remainder is 6 after subtracting 9 from 15.
Take the next digit (6) from the dividend and append it to 6, then repeat: 66 / 9

Let's proceed to step 5:
9 can be fit into 66 7 times, resulting in a remainder of 3.
Put 7 as the next digit of the answer. 
Result so far: 1117.0
Subtract 63 from 66 to get 3.
Take the next digit (6) from the dividend and append it to 3, then repeat: 36 / 9

Step 6:
9 goes into 36 4 times with a remainder of 0.
Record the quotient 4 as the next digit in the result. 
Result so far: 11174.0
If we take 36 away from 36, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Going ahead to step 7:
The number 9 fits into 0 0 times, leaving a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 11174.0
If we take 0 away from 0, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Moving on to step 8:
When dividing 0 by 9, we get 0 with a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 11174.0
Subtract 0 from 0 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

After the division, we end up with 11174.0 and a remainder of 0.0.