We divide 8101 by 18
We want to figure out the number of times 8101 can be divided by 18.

Going ahead to step 1:
If we divide 8 by 18, we get 0 and a remainder of 8.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 8 and we're left with 8.
Append the next digit (1) from the dividend to 8 and continue with: 81 / 18

Let's proceed to step 2:
If we divide 81 by 18, we get 4 and a remainder of 9.
Use 4 as the next digit of our solution. 
Result so far: 4.0
If we subtract 72 from 81, we get 9.
Append the next digit (0) from the dividend to 9 and continue with: 90 / 18

Step 3:
90 divided by 18 is 5 with a remainder of 0.
Record the quotient 5 as the next digit in the result. 
Result so far: 45.0
Subtracting 90 from 90 leaves us with 0.
Append the next digit (1) from the dividend to 0 and continue with: 1 / 18

Going ahead to step 4:
1 divided by 18 is 0 with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 450.0
If we subtract 0 from 1, 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.

Let's proceed to step 5:
If we divide 10 by 18, we get 0 and a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 450.0
The remainder is 10 after subtracting 0 from 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 6:
18 goes into 100 5 times with a remainder of 10.
Write down 5 as next digit of the result. 
Result so far: 450.05
Subtracting 90 from 100 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 7:
18 can be fit into 100 5 times, resulting in a remainder of 10.
The number 5 becomes the next digit in our result. 
Result so far: 450.055
Deduct 90 from 100 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

The quotient of the division is 450.055, and the remainder is 0.001.