Let's divide 10500 by 13
The aim is to understand the frequency of 13 in 10500.

On to step 1:
13 goes into 1 0 times with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 13

Going ahead to step 2:
If we divide 10 by 13, we get 0 and a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 10, we get 10.
Include the next digit (5) from the dividend after 10, then repeat: 105 / 13

Going ahead to step 3:
If we divide 105 by 13, we get 8 and a remainder of 1.
The next digit of our result is 8. 
Result so far: 8.0
The remainder is 1 after subtracting 104 from 105.
Fetch the next digit (0) from the dividend, attach it to 1 and continue: 10 / 13

Step 4:
13 can be fit into 10 0 times, resulting in a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 80.0
Subtracting 0 from 10 leaves us with 10.
Bring next digit (0) of the dividend behind the 10 and repeat the process: 100 / 13

Advancing to step 5:
100 divided by 13 is 7 with a remainder of 9.
The next digit of our result is 7. 
Result so far: 807.0
Deduct 91 from 100 and we're left 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.

On to step 6:
If we divide 90 by 13, we get 6 and a remainder of 12.
The number 6 becomes the next digit in our result. 
Result so far: 807.6
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.

Let's proceed to step 7:
13 can be fit into 120 9 times, resulting in a remainder of 3.
Record the quotient 9 as the next digit in the result. 
Result so far: 807.69
Subtracting 117 from 120 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.

Moving on to step 8:
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: 807.692
Subtract 26 from 30 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.

Advancing to step 9:
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: 807.6923
If we take 39 away from 40, 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.

On to step 10:
If we divide 10 by 13, we get 0 and a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 807.6923
If we subtract 0 from 10, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 11:
When dividing 100 by 13, we get 7 with a remainder of 9.
Write down 7 as next digit of the result. 
Result so far: 807.692307
If we take 91 away from 100, we end up 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.

Advancing to step 12:
90 divided by 13 is 6 with a remainder of 12.
Write down 6 as next digit of the result. 
Result so far: 807.6923076
Subtract 78 from 90 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Going ahead to step 13:
The number 13 fits into 120 9 times, leaving a remainder of 3.
Put 9 as the next digit of the answer. 
Result so far: 807.69230769
Subtracting 117 from 120 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.

Our division results in 807.69230769 with a remaining 3e-09.