91566 ÷ 27 
Our goal is to divide 91566 by 27.

Going ahead to step 1:
If we divide 9 by 27, we get 0 and a remainder of 9.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 9 and we're left with 9.
Grab the next digit (1) from the dividend, add it to 9, then carry on: 91 / 27

Moving on to step 2:
When dividing 91 by 27, we get 3 with a remainder of 10.
The next digit of our result is 3. 
Result so far: 3.0
If we take 81 away from 91, we end up with 10.
Fetch the next digit (5) from the dividend, attach it to 10 and continue: 105 / 27

Advancing to step 3:
If we divide 105 by 27, we get 3 and a remainder of 24.
Record the quotient 3 as the next digit in the result. 
Result so far: 33.0
The remainder is 24 after subtracting 81 from 105.
Include the next digit (6) from the dividend after 24, then repeat: 246 / 27

Advancing to step 4:
When dividing 246 by 27, we get 9 with a remainder of 3.
Write down 9 as next digit of the result. 
Result so far: 339.0
Subtracting 243 from 246 leaves us with 3.
Include the next digit (6) from the dividend after 3, then repeat: 36 / 27

Step 5:
If we divide 36 by 27, we get 1 and a remainder of 9.
Write down 1 as next digit of the result. 
Result so far: 3391.0
Deduct 27 from 36 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.

Step 6:
The number 27 fits into 90 3 times, leaving a remainder of 9.
Write down 3 as next digit of the result. 
Result so far: 3391.3
The remainder is 9 after subtracting 81 from 90.
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 7:
90 divided by 27 is 3 with a remainder of 9.
Record the quotient 3 as the next digit in the result. 
Result so far: 3391.33
Deduct 81 from 90 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.

The final result is 3391.33 with a remainder of 0.009.