We're dividing 565750 by 90 
The aim is to understand the frequency of 90 in 565750.

Advancing to step 1:
When dividing 5 by 90, we get 0 with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Include the next digit (6) from the dividend after 5, then repeat: 56 / 90

Let's proceed to step 2:
The number 90 fits into 56 0 times, leaving a remainder of 56.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 56, we end up with 56.
Grab the next digit (5) from the dividend, add it to 56, then carry on: 565 / 90

Step 3:
When dividing 565 by 90, we get 6 with a remainder of 25.
Write down 6 as next digit of the result. 
Result so far: 6.0
The remainder is 25 after subtracting 540 from 565.
Grab the next digit (7) from the dividend, add it to 25, then carry on: 257 / 90

Advancing to step 4:
90 goes into 257 2 times with a remainder of 77.
Write down 2 as next digit of the result. 
Result so far: 62.0
The remainder is 77 after subtracting 180 from 257.
Append the next digit (5) from the dividend to 77 and continue with: 775 / 90

Step 5:
The number 90 fits into 775 8 times, leaving a remainder of 55.
The next digit of our result is 8. 
Result so far: 628.0
The remainder is 55 after subtracting 720 from 775.
Append the next digit (0) from the dividend to 55 and continue with: 550 / 90

Going ahead to step 6:
When dividing 550 by 90, we get 6 with a remainder of 10.
The next digit of our result is 6. 
Result so far: 6286.0
The remainder is 10 after subtracting 540 from 550.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 7:
90 can be fit into 100 1 times, resulting in a remainder of 10.
Use 1 as the next digit of our solution. 
Result so far: 6286.1
Deduct 90 from 100 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 8:
The number 90 fits into 100 1 times, leaving a remainder of 10.
Write down 1 as next digit of the result. 
Result so far: 6286.11
Deduct 90 from 100 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.

The final result is 6286.11 with a remainder of 0.01.