We look at the division of 678251 by 79 
Our goal is to divide 678251 by 79.

Going ahead to step 1:
79 goes into 6 0 times with a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Append the next digit (7) from the dividend to 6 and continue with: 67 / 79

Let's proceed to step 2:
If we divide 67 by 79, we get 0 and a remainder of 67.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 67, we end up with 67.
Take the next digit (8) from the dividend and append it to 67, then repeat: 678 / 79

Let's proceed to step 3:
678 divided by 79 is 8 with a remainder of 46.
Use 8 as the next digit of our solution. 
Result so far: 8.0
Subtracting 632 from 678 leaves us with 46.
Include the next digit (2) from the dividend after 46, then repeat: 462 / 79

On to step 4:
462 divided by 79 is 5 with a remainder of 67.
Use 5 as the next digit of our solution. 
Result so far: 85.0
Deduct 395 from 462 and we're left with 67.
Append the next digit (5) from the dividend to 67 and continue with: 675 / 79

Step 5:
When dividing 675 by 79, we get 8 with a remainder of 43.
Write down 8 as next digit of the result. 
Result so far: 858.0
If we take 632 away from 675, we end up with 43.
Grab the next digit (1) from the dividend, add it to 43, then carry on: 431 / 79

On to step 6:
79 can be fit into 431 5 times, resulting in a remainder of 36.
The number 5 becomes the next digit in our result. 
Result so far: 8585.0
Subtract 395 from 431 to get 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Going ahead to step 7:
If we divide 360 by 79, we get 4 and a remainder of 44.
Record the quotient 4 as the next digit in the result. 
Result so far: 8585.4
If we subtract 316 from 360, we get 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Moving on to step 8:
The number 79 fits into 440 5 times, leaving a remainder of 45.
Put 5 as the next digit of the answer. 
Result so far: 8585.45
If we subtract 395 from 440, we get 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

Let's proceed to step 9:
79 goes into 450 5 times with a remainder of 55.
The next digit of our result is 5. 
Result so far: 8585.455
If we subtract 395 from 450, we get 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

In conclusion, the division gives 8585.455 with a balance of 0.0055.