We look at the division of 7683127 by 666 
Our goal is to divide 7683127 by 666.

Advancing to step 1:
666 goes into 7 0 times with a remainder of 7.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 7 to get 7.
Bring next digit (6) of the dividend behind the 7 and repeat the process: 76 / 666

Step 2:
If we divide 76 by 666, we get 0 and a remainder of 76.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 76 and we're left with 76.
Fetch the next digit (8) from the dividend, attach it to 76 and continue: 768 / 666

Advancing to step 3:
666 goes into 768 1 times with a remainder of 102.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we subtract 666 from 768, we get 102.
Bring next digit (3) of the dividend behind the 102 and repeat the process: 1023 / 666

Advancing to step 4:
666 can be fit into 1023 1 times, resulting in a remainder of 357.
Use 1 as the next digit of our solution. 
Result so far: 11.0
Deduct 666 from 1023 and we're left with 357.
Append the next digit (1) from the dividend to 357 and continue with: 3571 / 666

Step 5:
666 can be fit into 3571 5 times, resulting in a remainder of 241.
Write down 5 as next digit of the result. 
Result so far: 115.0
If we subtract 3330 from 3571, we get 241.
Take the next digit (2) from the dividend and append it to 241, then repeat: 2412 / 666

On to step 6:
The number 666 fits into 2412 3 times, leaving a remainder of 414.
The next digit of our result is 3. 
Result so far: 1153.0
If we take 1998 away from 2412, we end up with 414.
Take the next digit (7) from the dividend and append it to 414, then repeat: 4147 / 666

On to step 7:
666 can be fit into 4147 6 times, resulting in a remainder of 151.
The number 6 becomes the next digit in our result. 
Result so far: 11536.0
If we subtract 3996 from 4147, we get 151.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1510, and continue the process.

Step 8:
When dividing 1510 by 666, we get 2 with a remainder of 178.
The next digit of our result is 2. 
Result so far: 11536.2
Subtract 1332 from 1510 to get 178.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1780, and continue the process.

Advancing to step 9:
When dividing 1780 by 666, we get 2 with a remainder of 448.
Write down 2 as next digit of the result. 
Result so far: 11536.22
Deduct 1332 from 1780 and we're left with 448.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4480, and continue the process.

The final result is 11536.22 with a remainder of 0.448.