82186 ÷ 81 
The aim is to understand the frequency of 81 in 82186.

Going ahead to step 1:
The number 81 fits into 8 0 times, leaving a remainder of 8.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 8, we get 8.
Bring next digit (2) of the dividend behind the 8 and repeat the process: 82 / 81

Let's proceed to step 2:
When dividing 82 by 81, we get 1 with a remainder of 1.
The next digit of our result is 1. 
Result so far: 1.0
Subtracting 81 from 82 leaves us with 1.
Bring next digit (1) of the dividend behind the 1 and repeat the process: 11 / 81

Step 3:
11 divided by 81 is 0 with a remainder of 11.
Use 0 as the next digit of our solution. 
Result so far: 10.0
If we take 0 away from 11, we end up with 11.
Fetch the next digit (8) from the dividend, attach it to 11 and continue: 118 / 81

On to step 4:
The number 81 fits into 118 1 times, leaving a remainder of 37.
Use 1 as the next digit of our solution. 
Result so far: 101.0
If we take 81 away from 118, we end up with 37.
Grab the next digit (6) from the dividend, add it to 37, then carry on: 376 / 81

Moving on to step 5:
81 can be fit into 376 4 times, resulting in a remainder of 52.
Put 4 as the next digit of the answer. 
Result so far: 1014.0
Subtracting 324 from 376 leaves us with 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

Let's proceed to step 6:
81 can be fit into 520 6 times, resulting in a remainder of 34.
Put 6 as the next digit of the answer. 
Result so far: 1014.6
Subtracting 486 from 520 leaves us with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Advancing to step 7:
If we divide 340 by 81, we get 4 and a remainder of 16.
The next digit of our result is 4. 
Result so far: 1014.64
Subtract 324 from 340 to get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

On to step 8:
81 can be fit into 160 1 times, resulting in a remainder of 79.
The number 1 becomes the next digit in our result. 
Result so far: 1014.641
Subtract 81 from 160 to get 79.
Since there are no more digits in the dividend, we add a zero to the remainder making it 790, and continue the process.

Step 9:
If we divide 790 by 81, we get 9 and a remainder of 61.
The number 9 becomes the next digit in our result. 
Result so far: 1014.6419
Deduct 729 from 790 and we're left with 61.
Since there are no more digits in the dividend, we add a zero to the remainder making it 610, and continue the process.

Moving on to step 10:
610 divided by 81 is 7 with a remainder of 43.
Write down 7 as next digit of the result. 
Result so far: 1014.64197
Deduct 567 from 610 and we're left with 43.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

Step 11:
81 can be fit into 430 5 times, resulting in a remainder of 25.
Write down 5 as next digit of the result. 
Result so far: 1014.641975
If we subtract 405 from 430, we get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Advancing to step 12:
81 can be fit into 250 3 times, resulting in a remainder of 7.
Record the quotient 3 as the next digit in the result. 
Result so far: 1014.6419753
Subtracting 243 from 250 leaves us with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Going ahead to step 13:
81 can be fit into 70 0 times, resulting in a remainder of 70.
The next digit of our result is 0. 
Result so far: 1014.6419753
Subtracting 0 from 70 leaves us with 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

In conclusion, the division gives 1014.6419753 with a balance of 7e-08.