55581249 ÷ 503 
The aim is to understand the frequency of 503 in 55581249.

Moving on to step 1:
The number 503 fits into 5 0 times, leaving a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Take the next digit (5) from the dividend and append it to 5, then repeat: 55 / 503

Step 2:
The number 503 fits into 55 0 times, leaving a remainder of 55.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 55 after subtracting 0 from 55.
Fetch the next digit (5) from the dividend, attach it to 55 and continue: 555 / 503

Moving on to step 3:
555 divided by 503 is 1 with a remainder of 52.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
The remainder is 52 after subtracting 503 from 555.
Fetch the next digit (8) from the dividend, attach it to 52 and continue: 528 / 503

Advancing to step 4:
503 goes into 528 1 times with a remainder of 25.
The number 1 becomes the next digit in our result. 
Result so far: 11.0
If we subtract 503 from 528, we get 25.
Bring next digit (1) of the dividend behind the 25 and repeat the process: 251 / 503

Let's proceed to step 5:
When dividing 251 by 503, we get 0 with a remainder of 251.
The next digit of our result is 0. 
Result so far: 110.0
Deduct 0 from 251 and we're left with 251.
Include the next digit (2) from the dividend after 251, then repeat: 2512 / 503

Advancing to step 6:
If we divide 2512 by 503, we get 4 and a remainder of 500.
Put 4 as the next digit of the answer. 
Result so far: 1104.0
Subtracting 2012 from 2512 leaves us with 500.
Append the next digit (4) from the dividend to 500 and continue with: 5004 / 503

On to step 7:
503 can be fit into 5004 9 times, resulting in a remainder of 477.
Record the quotient 9 as the next digit in the result. 
Result so far: 11049.0
If we take 4527 away from 5004, we end up with 477.
Grab the next digit (9) from the dividend, add it to 477, then carry on: 4779 / 503

Going ahead to step 8:
If we divide 4779 by 503, we get 9 and a remainder of 252.
The next digit of our result is 9. 
Result so far: 110499.0
The remainder is 252 after subtracting 4527 from 4779.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2520, and continue the process.

Step 9:
503 can be fit into 2520 5 times, resulting in a remainder of 5.
Record the quotient 5 as the next digit in the result. 
Result so far: 110499.5
Deduct 2515 from 2520 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 10:
The number 503 fits into 50 0 times, leaving a remainder of 50.
Put 0 as the next digit of the answer. 
Result so far: 110499.5
If we subtract 0 from 50, we get 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Moving on to step 11:
503 can be fit into 500 0 times, resulting in a remainder of 500.
Record the quotient 0 as the next digit in the result. 
Result so far: 110499.5
If we take 0 away from 500, we end up with 500.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5000, and continue the process.

After the division, we end up with 110499.5 and a remainder of 0.05.