We look at the division of 6878 by 6 
Let's see how many times 6 fits into 6878.

Advancing to step 1:
The number 6 fits into 6 1 times, leaving a remainder of 0.
Write down 1 as next digit of the result. 
Result so far: 1.0
The remainder is 0 after subtracting 6 from 6.
Include the next digit (8) from the dividend after 0, then repeat: 8 / 6

Going ahead to step 2:
The number 6 fits into 8 1 times, leaving a remainder of 2.
Put 1 as the next digit of the answer. 
Result so far: 11.0
Subtract 6 from 8 to get 2.
Append the next digit (7) from the dividend to 2 and continue with: 27 / 6

Step 3:
If we divide 27 by 6, we get 4 and a remainder of 3.
Put 4 as the next digit of the answer. 
Result so far: 114.0
The remainder is 3 after subtracting 24 from 27.
Grab the next digit (8) from the dividend, add it to 3, then carry on: 38 / 6

Step 4:
6 goes into 38 6 times with a remainder of 2.
The next digit of our result is 6. 
Result so far: 1146.0
Subtracting 36 from 38 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 5:
When dividing 20 by 6, we get 3 with a remainder of 2.
Record the quotient 3 as the next digit in the result. 
Result so far: 1146.3
Deduct 18 from 20 and we're left with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Going ahead to step 6:
The number 6 fits into 20 3 times, leaving a remainder of 2.
Put 3 as the next digit of the answer. 
Result so far: 1146.33
If we subtract 18 from 20, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

After the division, we end up with 1146.33 and a remainder of 0.002.