We're dividing 100218 by 81 
The aim is to understand the frequency of 81 in 100218.

Step 1:
81 goes into 1 0 times with a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Fetch the next digit (0) from the dividend, attach it to 1 and continue: 10 / 81

On to step 2:
81 goes into 10 0 times with a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 10 after subtracting 0 from 10.
Append the next digit (0) from the dividend to 10 and continue with: 100 / 81

Let's proceed to step 3:
If we divide 100 by 81, we get 1 and a remainder of 19.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
The remainder is 19 after subtracting 81 from 100.
Append the next digit (2) from the dividend to 19 and continue with: 192 / 81

Going ahead to step 4:
81 can be fit into 192 2 times, resulting in a remainder of 30.
The number 2 becomes the next digit in our result. 
Result so far: 12.0
If we take 162 away from 192, we end up with 30.
Append the next digit (1) from the dividend to 30 and continue with: 301 / 81

Moving on to step 5:
301 divided by 81 is 3 with a remainder of 58.
Put 3 as the next digit of the answer. 
Result so far: 123.0
If we take 243 away from 301, we end up with 58.
Fetch the next digit (8) from the dividend, attach it to 58 and continue: 588 / 81

On to step 6:
81 goes into 588 7 times with a remainder of 21.
Put 7 as the next digit of the answer. 
Result so far: 1237.0
The remainder is 21 after subtracting 567 from 588.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Advancing to step 7:
210 divided by 81 is 2 with a remainder of 48.
Use 2 as the next digit of our solution. 
Result so far: 1237.2
Subtract 162 from 210 to get 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

Let's proceed to step 8:
81 can be fit into 480 5 times, resulting in a remainder of 75.
The next digit of our result is 5. 
Result so far: 1237.25
Deduct 405 from 480 and we're left with 75.
Since there are no more digits in the dividend, we add a zero to the remainder making it 750, and continue the process.

Advancing to step 9:
750 divided by 81 is 9 with a remainder of 21.
Put 9 as the next digit of the answer. 
Result so far: 1237.259
Subtracting 729 from 750 leaves us with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Step 10:
When dividing 210 by 81, we get 2 with a remainder of 48.
Put 2 as the next digit of the answer. 
Result so far: 1237.2592
The remainder is 48 after subtracting 162 from 210.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

On to step 11:
If we divide 480 by 81, we get 5 and a remainder of 75.
The number 5 becomes the next digit in our result. 
Result so far: 1237.25925
If we subtract 405 from 480, we get 75.
Since there are no more digits in the dividend, we add a zero to the remainder making it 750, and continue the process.

Moving on to step 12:
When dividing 750 by 81, we get 9 with a remainder of 21.
Record the quotient 9 as the next digit in the result. 
Result so far: 1237.259259
Deduct 729 from 750 and we're left with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Going ahead to step 13:
81 can be fit into 210 2 times, resulting in a remainder of 48.
The number 2 becomes the next digit in our result. 
Result so far: 1237.2592592
If we take 162 away from 210, we end up with 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

Advancing to step 14:
480 divided by 81 is 5 with a remainder of 75.
The number 5 becomes the next digit in our result. 
Result so far: 1237.25925925
The remainder is 75 after subtracting 405 from 480.
Since there are no more digits in the dividend, we add a zero to the remainder making it 750, and continue the process.

Our division results in 1237.25925925 with a remaining 7.5e-08.