We're dividing 9021 by 8 
We're looking to find how many times 8 goes into 9021.

Advancing to step 1:
When dividing 9 by 8, we get 1 with a remainder of 1.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
The remainder is 1 after subtracting 8 from 9.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 8

Let's proceed to step 2:
8 goes into 10 1 times with a remainder of 2.
Write down 1 as next digit of the result. 
Result so far: 11.0
If we take 8 away from 10, we end up with 2.
Fetch the next digit (2) from the dividend, attach it to 2 and continue: 22 / 8

Step 3:
The number 8 fits into 22 2 times, leaving a remainder of 6.
The next digit of our result is 2. 
Result so far: 112.0
If we subtract 16 from 22, we get 6.
Fetch the next digit (1) from the dividend, attach it to 6 and continue: 61 / 8

Moving on to step 4:
If we divide 61 by 8, we get 7 and a remainder of 5.
The next digit of our result is 7. 
Result so far: 1127.0
Deduct 56 from 61 and we're left with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Going ahead to step 5:
If we divide 50 by 8, we get 6 and a remainder of 2.
Use 6 as the next digit of our solution. 
Result so far: 1127.6
If we subtract 48 from 50, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 6:
If we divide 20 by 8, we get 2 and a remainder of 4.
The next digit of our result is 2. 
Result so far: 1127.62
Subtract 16 from 20 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 7:
When dividing 40 by 8, we get 5 with a remainder of 0.
The next digit of our result is 5. 
Result so far: 1127.625
Subtracting 40 from 40 leaves us 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.

Step 8:
8 goes into 0 0 times with a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 1127.625
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.

Going ahead to step 9:
The number 8 fits into 0 0 times, leaving a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 1127.625
Subtracting 0 from 0 leaves us 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.

The quotient of the division is 1127.625, and the remainder is 0.0.