We look at the division of 127966 by 3 
Our goal is to divide 127966 by 3.

Advancing to step 1:
If we divide 1 by 3, we get 0 and a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Bring next digit (2) of the dividend behind the 1 and repeat the process: 12 / 3

Let's proceed to step 2:
12 divided by 3 is 4 with a remainder of 0.
The next digit of our result is 4. 
Result so far: 4.0
The remainder is 0 after subtracting 12 from 12.
Append the next digit (7) from the dividend to 0 and continue with: 7 / 3

Advancing to step 3:
3 goes into 7 2 times with a remainder of 1.
Use 2 as the next digit of our solution. 
Result so far: 42.0
Subtracting 6 from 7 leaves us with 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 3

Moving on to step 4:
19 divided by 3 is 6 with a remainder of 1.
Use 6 as the next digit of our solution. 
Result so far: 426.0
Deduct 18 from 19 and we're left with 1.
Append the next digit (6) from the dividend to 1 and continue with: 16 / 3

Step 5:
If we divide 16 by 3, we get 5 and a remainder of 1.
Put 5 as the next digit of the answer. 
Result so far: 4265.0
The remainder is 1 after subtracting 15 from 16.
Append the next digit (6) from the dividend to 1 and continue with: 16 / 3

Going ahead to step 6:
If we divide 16 by 3, we get 5 and a remainder of 1.
Use 5 as the next digit of our solution. 
Result so far: 42655.0
Subtracting 15 from 16 leaves us with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 7:
The number 3 fits into 10 3 times, leaving a remainder of 1.
The next digit of our result is 3. 
Result so far: 42655.3
If we take 9 away from 10, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Going ahead to step 8:
3 can be fit into 10 3 times, resulting in a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 42655.33
If we take 9 away from 10, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

In conclusion, the division gives 42655.33 with a balance of 0.001.