102905 ÷ 13 
The aim is to understand the frequency of 13 in 102905.

Moving on to step 1:
The number 13 fits into 1 0 times, leaving a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Grab the next digit (0) from the dividend, add it to 1, then carry on: 10 / 13

On to step 2:
The number 13 fits into 10 0 times, leaving a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 10 and we're left with 10.
Grab the next digit (2) from the dividend, add it to 10, then carry on: 102 / 13

Moving on to step 3:
When dividing 102 by 13, we get 7 with a remainder of 11.
Write down 7 as next digit of the result. 
Result so far: 7.0
Deduct 91 from 102 and we're left with 11.
Bring next digit (9) of the dividend behind the 11 and repeat the process: 119 / 13

Advancing to step 4:
The number 13 fits into 119 9 times, leaving a remainder of 2.
The number 9 becomes the next digit in our result. 
Result so far: 79.0
If we subtract 117 from 119, we get 2.
Take the next digit (0) from the dividend and append it to 2, then repeat: 20 / 13

Going ahead to step 5:
13 can be fit into 20 1 times, resulting in a remainder of 7.
The next digit of our result is 1. 
Result so far: 791.0
Deduct 13 from 20 and we're left with 7.
Take the next digit (5) from the dividend and append it to 7, then repeat: 75 / 13

Going ahead to step 6:
75 divided by 13 is 5 with a remainder of 10.
Put 5 as the next digit of the answer. 
Result so far: 7915.0
Deduct 65 from 75 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.

Let's proceed to step 7:
13 can be fit into 100 7 times, resulting in a remainder of 9.
Use 7 as the next digit of our solution. 
Result so far: 7915.7
The remainder is 9 after subtracting 91 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

On to step 8:
When dividing 90 by 13, we get 6 with a remainder of 12.
Put 6 as the next digit of the answer. 
Result so far: 7915.76
The remainder is 12 after subtracting 78 from 90.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Advancing to step 9:
13 goes into 120 9 times with a remainder of 3.
Write down 9 as next digit of the result. 
Result so far: 7915.769
If we take 117 away from 120, we end up 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.

Moving on to step 10:
When dividing 30 by 13, we get 2 with a remainder of 4.
Write down 2 as next digit of the result. 
Result so far: 7915.7692
If we take 26 away from 30, we end up with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 11:
When dividing 40 by 13, we get 3 with a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 7915.76923
Subtracting 39 from 40 leaves us 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.

Let's proceed to step 12:
When dividing 10 by 13, we get 0 with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 7915.76923
Subtracting 0 from 10 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.

Advancing to step 13:
13 can be fit into 100 7 times, resulting in a remainder of 9.
The number 7 becomes the next digit in our result. 
Result so far: 7915.7692307
Subtracting 91 from 100 leaves us with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Step 14:
When dividing 90 by 13, we get 6 with a remainder of 12.
Write down 6 as next digit of the result. 
Result so far: 7915.76923076
If we take 78 away from 90, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

The final result is 7915.76923076 with a remainder of 1.2e-08.