We're dividing 555 by 61 
We want to figure out the number of times 555 can be divided by 61.

Moving on to step 1:
If we divide 5 by 61, we get 0 and a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Append the next digit (5) from the dividend to 5 and continue with: 55 / 61

Advancing to step 2:
61 can be fit into 55 0 times, resulting in a remainder of 55.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 55 to get 55.
Fetch the next digit (5) from the dividend, attach it to 55 and continue: 555 / 61

Step 3:
61 can be fit into 555 9 times, resulting in a remainder of 6.
Write down 9 as next digit of the result. 
Result so far: 9.0
If we subtract 549 from 555, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

On to step 4:
The number 61 fits into 60 0 times, leaving a remainder of 60.
Record the quotient 0 as the next digit in the result. 
Result so far: 9.0
The remainder is 60 after subtracting 0 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Going ahead to step 5:
When dividing 600 by 61, we get 9 with a remainder of 51.
The next digit of our result is 9. 
Result so far: 9.09
If we take 549 away from 600, we end up with 51.
Since there are no more digits in the dividend, we add a zero to the remainder making it 510, and continue the process.

Going ahead to step 6:
61 can be fit into 510 8 times, resulting in a remainder of 22.
Put 8 as the next digit of the answer. 
Result so far: 9.098
Deduct 488 from 510 and we're left with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Moving on to step 7:
61 goes into 220 3 times with a remainder of 37.
Use 3 as the next digit of our solution. 
Result so far: 9.0983
Deduct 183 from 220 and we're left with 37.
Since there are no more digits in the dividend, we add a zero to the remainder making it 370, and continue the process.

Going ahead to step 8:
370 divided by 61 is 6 with a remainder of 4.
The number 6 becomes the next digit in our result. 
Result so far: 9.09836
The remainder is 4 after subtracting 366 from 370.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Advancing to step 9:
When dividing 40 by 61, we get 0 with a remainder of 40.
The number 0 becomes the next digit in our result. 
Result so far: 9.09836
Subtracting 0 from 40 leaves us with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Advancing to step 10:
When dividing 400 by 61, we get 6 with a remainder of 34.
Use 6 as the next digit of our solution. 
Result so far: 9.0983606
Deduct 366 from 400 and we're left with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

On to step 11:
The number 61 fits into 340 5 times, leaving a remainder of 35.
The number 5 becomes the next digit in our result. 
Result so far: 9.09836065
Subtracting 305 from 340 leaves us with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

After the division, we end up with 9.09836065 and a remainder of 3.5e-08.