5275509 ÷ 501 
The aim is to understand the frequency of 501 in 5275509.

Step 1:
When dividing 5 by 501, we get 0 with a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Append the next digit (2) from the dividend to 5 and continue with: 52 / 501

On to step 2:
52 divided by 501 is 0 with a remainder of 52.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 52, we end up with 52.
Bring next digit (7) of the dividend behind the 52 and repeat the process: 527 / 501

Moving on to step 3:
501 can be fit into 527 1 times, resulting in a remainder of 26.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
If we take 501 away from 527, we end up with 26.
Include the next digit (5) from the dividend after 26, then repeat: 265 / 501

Let's proceed to step 4:
501 goes into 265 0 times with a remainder of 265.
The number 0 becomes the next digit in our result. 
Result so far: 10.0
Deduct 0 from 265 and we're left with 265.
Include the next digit (5) from the dividend after 265, then repeat: 2655 / 501

Going ahead to step 5:
The number 501 fits into 2655 5 times, leaving a remainder of 150.
Record the quotient 5 as the next digit in the result. 
Result so far: 105.0
If we take 2505 away from 2655, we end up with 150.
Take the next digit (0) from the dividend and append it to 150, then repeat: 1500 / 501

Going ahead to step 6:
When dividing 1500 by 501, we get 2 with a remainder of 498.
The number 2 becomes the next digit in our result. 
Result so far: 1052.0
If we subtract 1002 from 1500, we get 498.
Take the next digit (9) from the dividend and append it to 498, then repeat: 4989 / 501

On to step 7:
501 goes into 4989 9 times with a remainder of 480.
Use 9 as the next digit of our solution. 
Result so far: 10529.0
Subtracting 4509 from 4989 leaves us with 480.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4800, and continue the process.

Going ahead to step 8:
When dividing 4800 by 501, we get 9 with a remainder of 291.
Write down 9 as next digit of the result. 
Result so far: 10529.9
If we take 4509 away from 4800, we end up with 291.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2910, and continue the process.

On to step 9:
If we divide 2910 by 501, we get 5 and a remainder of 405.
Use 5 as the next digit of our solution. 
Result so far: 10529.95
If we take 2505 away from 2910, we end up with 405.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4050, and continue the process.

Advancing to step 10:
When dividing 4050 by 501, we get 8 with a remainder of 42.
Put 8 as the next digit of the answer. 
Result so far: 10529.958
If we take 4008 away from 4050, we end up with 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Moving on to step 11:
420 divided by 501 is 0 with a remainder of 420.
Write down 0 as next digit of the result. 
Result so far: 10529.958
If we subtract 0 from 420, we get 420.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4200, and continue the process.

Moving on to step 12:
501 goes into 4200 8 times with a remainder of 192.
The number 8 becomes the next digit in our result. 
Result so far: 10529.95808
If we take 4008 away from 4200, we end up with 192.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1920, and continue the process.

Let's proceed to step 13:
501 can be fit into 1920 3 times, resulting in a remainder of 417.
Use 3 as the next digit of our solution. 
Result so far: 10529.958083
If we subtract 1503 from 1920, we get 417.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4170, and continue the process.

Let's proceed to step 14:
The number 501 fits into 4170 8 times, leaving a remainder of 162.
Use 8 as the next digit of our solution. 
Result so far: 10529.9580838
Subtracting 4008 from 4170 leaves us with 162.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1620, and continue the process.

Advancing to step 15:
When dividing 1620 by 501, we get 3 with a remainder of 117.
Write down 3 as next digit of the result. 
Result so far: 10529.95808383
If we take 1503 away from 1620, we end up with 117.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1170, and continue the process.

The final result is 10529.95808383 with a remainder of 1.17e-07.