We look at the division of 4278 by 51 
We're looking to find how many times 51 goes into 4278.

Advancing to step 1:
If we divide 4 by 51, we get 0 and a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 4 after subtracting 0 from 4.
Append the next digit (2) from the dividend to 4 and continue with: 42 / 51

Step 2:
When dividing 42 by 51, we get 0 with a remainder of 42.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 42 leaves us with 42.
Take the next digit (7) from the dividend and append it to 42, then repeat: 427 / 51

Advancing to step 3:
51 can be fit into 427 8 times, resulting in a remainder of 19.
Record the quotient 8 as the next digit in the result. 
Result so far: 8.0
The remainder is 19 after subtracting 408 from 427.
Include the next digit (8) from the dividend after 19, then repeat: 198 / 51

Advancing to step 4:
When dividing 198 by 51, we get 3 with a remainder of 45.
Use 3 as the next digit of our solution. 
Result so far: 83.0
If we take 153 away from 198, 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 5:
450 divided by 51 is 8 with a remainder of 42.
Write down 8 as next digit of the result. 
Result so far: 83.8
If we subtract 408 from 450, we get 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

On to step 6:
The number 51 fits into 420 8 times, leaving a remainder of 12.
The next digit of our result is 8. 
Result so far: 83.88
Subtracting 408 from 420 leaves us 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.

After the division, we end up with 83.88 and a remainder of 0.012.