We're dividing 100566 by 51 
We're looking to find how many times 51 goes into 100566.

Moving on to step 1:
51 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Append the next digit (0) from the dividend to 1 and continue with: 10 / 51

Going ahead to step 2:
The number 51 fits into 10 0 times, leaving a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 10, we get 10.
Fetch the next digit (0) from the dividend, attach it to 10 and continue: 100 / 51

Going ahead to step 3:
When dividing 100 by 51, we get 1 with a remainder of 49.
The next digit of our result is 1. 
Result so far: 1.0
The remainder is 49 after subtracting 51 from 100.
Include the next digit (5) from the dividend after 49, then repeat: 495 / 51

On to step 4:
51 goes into 495 9 times with a remainder of 36.
Record the quotient 9 as the next digit in the result. 
Result so far: 19.0
If we subtract 459 from 495, we get 36.
Include the next digit (6) from the dividend after 36, then repeat: 366 / 51

Going ahead to step 5:
366 divided by 51 is 7 with a remainder of 9.
Use 7 as the next digit of our solution. 
Result so far: 197.0
Subtract 357 from 366 to get 9.
Grab the next digit (6) from the dividend, add it to 9, then carry on: 96 / 51

Going ahead to step 6:
51 goes into 96 1 times with a remainder of 45.
Use 1 as the next digit of our solution. 
Result so far: 1971.0
If we take 51 away from 96, we end up with 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

Going ahead to step 7:
If we divide 450 by 51, we get 8 and a remainder of 42.
Record the quotient 8 as the next digit in the result. 
Result so far: 1971.8
Deduct 408 from 450 and we're left 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.

Advancing to step 8:
If we divide 420 by 51, we get 8 and a remainder of 12.
Write down 8 as next digit of the result. 
Result so far: 1971.88
If we take 408 away from 420, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

In conclusion, the division gives 1971.88 with a balance of 0.012.