813209 ÷ 7 
The aim is to understand the frequency of 7 in 813209.

Let's proceed to step 1:
When dividing 8 by 7, we get 1 with a remainder of 1.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
The remainder is 1 after subtracting 7 from 8.
Append the next digit (1) from the dividend to 1 and continue with: 11 / 7

Let's proceed to step 2:
If we divide 11 by 7, we get 1 and a remainder of 4.
Use 1 as the next digit of our solution. 
Result so far: 11.0
Subtract 7 from 11 to get 4.
Take the next digit (3) from the dividend and append it to 4, then repeat: 43 / 7

Going ahead to step 3:
7 goes into 43 6 times with a remainder of 1.
The number 6 becomes the next digit in our result. 
Result so far: 116.0
The remainder is 1 after subtracting 42 from 43.
Append the next digit (2) from the dividend to 1 and continue with: 12 / 7

Moving on to step 4:
The number 7 fits into 12 1 times, leaving a remainder of 5.
Record the quotient 1 as the next digit in the result. 
Result so far: 1161.0
The remainder is 5 after subtracting 7 from 12.
Grab the next digit (0) from the dividend, add it to 5, then carry on: 50 / 7

On to step 5:
7 goes into 50 7 times with a remainder of 1.
Use 7 as the next digit of our solution. 
Result so far: 11617.0
If we take 49 away from 50, we end up with 1.
Take the next digit (9) from the dividend and append it to 1, then repeat: 19 / 7

Step 6:
If we divide 19 by 7, we get 2 and a remainder of 5.
Put 2 as the next digit of the answer. 
Result so far: 116172.0
The remainder is 5 after subtracting 14 from 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 7:
50 divided by 7 is 7 with a remainder of 1.
Write down 7 as next digit of the result. 
Result so far: 116172.7
If we take 49 away from 50, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 8:
When dividing 10 by 7, we get 1 with a remainder of 3.
The number 1 becomes the next digit in our result. 
Result so far: 116172.71
Subtracting 7 from 10 leaves us with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

On to step 9:
7 goes into 30 4 times with a remainder of 2.
Record the quotient 4 as the next digit in the result. 
Result so far: 116172.714
If we take 28 away from 30, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 10:
If we divide 20 by 7, we get 2 and a remainder of 6.
Put 2 as the next digit of the answer. 
Result so far: 116172.7142
The remainder is 6 after subtracting 14 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Advancing to step 11:
7 can be fit into 60 8 times, resulting in a remainder of 4.
Record the quotient 8 as the next digit in the result. 
Result so far: 116172.71428
The remainder is 4 after subtracting 56 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

On to step 12:
The number 7 fits into 40 5 times, leaving a remainder of 5.
The next digit of our result is 5. 
Result so far: 116172.714285
Deduct 35 from 40 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.

Moving on to step 13:
When dividing 50 by 7, we get 7 with a remainder of 1.
The number 7 becomes the next digit in our result. 
Result so far: 116172.7142857
Subtract 49 from 50 to 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.

On to step 14:
If we divide 10 by 7, we get 1 and a remainder of 3.
Use 1 as the next digit of our solution. 
Result so far: 116172.71428571
Subtracting 7 from 10 leaves us with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

In conclusion, the division gives 116172.71428571 with a balance of 3e-09.