We're dividing 516671 by 127 
Let's see how many times 127 fits into 516671.

Going ahead to step 1:
The number 127 fits into 5 0 times, leaving a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Include the next digit (1) from the dividend after 5, then repeat: 51 / 127

Moving on to step 2:
The number 127 fits into 51 0 times, leaving a remainder of 51.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 51 after subtracting 0 from 51.
Fetch the next digit (6) from the dividend, attach it to 51 and continue: 516 / 127

Let's proceed to step 3:
If we divide 516 by 127, we get 4 and a remainder of 8.
Put 4 as the next digit of the answer. 
Result so far: 4.0
If we subtract 508 from 516, we get 8.
Include the next digit (6) from the dividend after 8, then repeat: 86 / 127

Advancing to step 4:
When dividing 86 by 127, we get 0 with a remainder of 86.
Write down 0 as next digit of the result. 
Result so far: 40.0
Subtract 0 from 86 to get 86.
Take the next digit (7) from the dividend and append it to 86, then repeat: 867 / 127

On to step 5:
867 divided by 127 is 6 with a remainder of 105.
Use 6 as the next digit of our solution. 
Result so far: 406.0
If we take 762 away from 867, we end up with 105.
Take the next digit (1) from the dividend and append it to 105, then repeat: 1051 / 127

Going ahead to step 6:
If we divide 1051 by 127, we get 8 and a remainder of 35.
Write down 8 as next digit of the result. 
Result so far: 4068.0
If we take 1016 away from 1051, we end up 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.

Going ahead to step 7:
127 can be fit into 350 2 times, resulting in a remainder of 96.
The next digit of our result is 2. 
Result so far: 4068.2
Deduct 254 from 350 and we're left with 96.
Since there are no more digits in the dividend, we add a zero to the remainder making it 960, and continue the process.

Going ahead to step 8:
960 divided by 127 is 7 with a remainder of 71.
The number 7 becomes the next digit in our result. 
Result so far: 4068.27
The remainder is 71 after subtracting 889 from 960.
Since there are no more digits in the dividend, we add a zero to the remainder making it 710, and continue the process.

Going ahead to step 9:
127 can be fit into 710 5 times, resulting in a remainder of 75.
Write down 5 as next digit of the result. 
Result so far: 4068.275
If we subtract 635 from 710, we get 75.
Since there are no more digits in the dividend, we add a zero to the remainder making it 750, and continue the process.

Moving on to step 10:
750 divided by 127 is 5 with a remainder of 115.
The number 5 becomes the next digit in our result. 
Result so far: 4068.2755
Subtract 635 from 750 to get 115.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1150, and continue the process.

In conclusion, the division gives 4068.2755 with a balance of 0.00115.