We're dividing 816628 by 81 
The aim is to understand the frequency of 81 in 816628.

Advancing to step 1:
8 divided by 81 is 0 with a remainder of 8.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 8 to get 8.
Take the next digit (1) from the dividend and append it to 8, then repeat: 81 / 81

On to step 2:
If we divide 81 by 81, we get 1 and a remainder of 0.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtracting 81 from 81 leaves us with 0.
Grab the next digit (6) from the dividend, add it to 0, then carry on: 6 / 81

Moving on to step 3:
If we divide 6 by 81, we get 0 and a remainder of 6.
The next digit of our result is 0. 
Result so far: 10.0
Deduct 0 from 6 and we're left with 6.
Include the next digit (6) from the dividend after 6, then repeat: 66 / 81

Let's proceed to step 4:
The number 81 fits into 66 0 times, leaving a remainder of 66.
Use 0 as the next digit of our solution. 
Result so far: 100.0
The remainder is 66 after subtracting 0 from 66.
Append the next digit (2) from the dividend to 66 and continue with: 662 / 81

Step 5:
81 can be fit into 662 8 times, resulting in a remainder of 14.
Put 8 as the next digit of the answer. 
Result so far: 1008.0
Deduct 648 from 662 and we're left with 14.
Fetch the next digit (8) from the dividend, attach it to 14 and continue: 148 / 81

On to step 6:
81 can be fit into 148 1 times, resulting in a remainder of 67.
The number 1 becomes the next digit in our result. 
Result so far: 10081.0
If we subtract 81 from 148, we get 67.
Since there are no more digits in the dividend, we add a zero to the remainder making it 670, and continue the process.

Advancing to step 7:
81 goes into 670 8 times with a remainder of 22.
Use 8 as the next digit of our solution. 
Result so far: 10081.8
Subtract 648 from 670 to get 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

On to step 8:
220 divided by 81 is 2 with a remainder of 58.
Use 2 as the next digit of our solution. 
Result so far: 10081.82
Subtract 162 from 220 to get 58.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

On to step 9:
81 goes into 580 7 times with a remainder of 13.
Put 7 as the next digit of the answer. 
Result so far: 10081.827
The remainder is 13 after subtracting 567 from 580.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Going ahead to step 10:
81 can be fit into 130 1 times, resulting in a remainder of 49.
Put 1 as the next digit of the answer. 
Result so far: 10081.8271
If we take 81 away from 130, we end up with 49.
Since there are no more digits in the dividend, we add a zero to the remainder making it 490, and continue the process.

Advancing to step 11:
When dividing 490 by 81, we get 6 with a remainder of 4.
The next digit of our result is 6. 
Result so far: 10081.82716
Subtract 486 from 490 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 12:
The number 81 fits into 40 0 times, leaving a remainder of 40.
Write down 0 as next digit of the result. 
Result so far: 10081.82716
Subtracting 0 from 40 leaves us with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Step 13:
81 goes into 400 4 times with a remainder of 76.
Put 4 as the next digit of the answer. 
Result so far: 10081.8271604
If we subtract 324 from 400, we get 76.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

Going ahead to step 14:
If we divide 760 by 81, we get 9 and a remainder of 31.
Use 9 as the next digit of our solution. 
Result so far: 10081.82716049
Deduct 729 from 760 and we're left with 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Our division results in 10081.82716049 with a remaining 3.1e-08.