We're dividing 1088628 by 511 
The aim is to understand the frequency of 511 in 1088628.

Advancing to step 1:
When dividing 1 by 511, we get 0 with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
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 / 511

Let's proceed to step 2:
If we divide 10 by 511, we get 0 and a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 10 leaves us with 10.
Take the next digit (8) from the dividend and append it to 10, then repeat: 108 / 511

Advancing to step 3:
511 can be fit into 108 0 times, resulting in a remainder of 108.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 108 to get 108.
Grab the next digit (8) from the dividend, add it to 108, then carry on: 1088 / 511

Let's proceed to step 4:
1088 divided by 511 is 2 with a remainder of 66.
The next digit of our result is 2. 
Result so far: 2.0
Subtract 1022 from 1088 to get 66.
Include the next digit (6) from the dividend after 66, then repeat: 666 / 511

Moving on to step 5:
If we divide 666 by 511, we get 1 and a remainder of 155.
Use 1 as the next digit of our solution. 
Result so far: 21.0
If we subtract 511 from 666, we get 155.
Append the next digit (2) from the dividend to 155 and continue with: 1552 / 511

On to step 6:
511 goes into 1552 3 times with a remainder of 19.
The next digit of our result is 3. 
Result so far: 213.0
Deduct 1533 from 1552 and we're left with 19.
Take the next digit (8) from the dividend and append it to 19, then repeat: 198 / 511

Moving on to step 7:
When dividing 198 by 511, we get 0 with a remainder of 198.
Write down 0 as next digit of the result. 
Result so far: 2130.0
The remainder is 198 after subtracting 0 from 198.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1980, and continue the process.

Advancing to step 8:
1980 divided by 511 is 3 with a remainder of 447.
Use 3 as the next digit of our solution. 
Result so far: 2130.3
If we subtract 1533 from 1980, we get 447.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4470, and continue the process.

Going ahead to step 9:
If we divide 4470 by 511, we get 8 and a remainder of 382.
The number 8 becomes the next digit in our result. 
Result so far: 2130.38
Subtract 4088 from 4470 to get 382.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3820, and continue the process.

On to step 10:
3820 divided by 511 is 7 with a remainder of 243.
Use 7 as the next digit of our solution. 
Result so far: 2130.387
If we take 3577 away from 3820, we end up with 243.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2430, and continue the process.

On to step 11:
511 can be fit into 2430 4 times, resulting in a remainder of 386.
The number 4 becomes the next digit in our result. 
Result so far: 2130.3874
Subtracting 2044 from 2430 leaves us with 386.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3860, and continue the process.

Step 12:
When dividing 3860 by 511, we get 7 with a remainder of 283.
The number 7 becomes the next digit in our result. 
Result so far: 2130.38747
Subtract 3577 from 3860 to get 283.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2830, and continue the process.

Step 13:
The number 511 fits into 2830 5 times, leaving a remainder of 275.
The next digit of our result is 5. 
Result so far: 2130.387475
Subtracting 2555 from 2830 leaves us with 275.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2750, and continue the process.

Going ahead to step 14:
When dividing 2750 by 511, we get 5 with a remainder of 195.
Record the quotient 5 as the next digit in the result. 
Result so far: 2130.3874755
If we take 2555 away from 2750, we end up with 195.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1950, and continue the process.

After the division, we end up with 2130.3874755 and a remainder of 1.95e-06.