We divide 679125 by 27
We're looking to find how many times 27 goes into 679125.

Moving on to step 1:
27 can be fit into 6 0 times, resulting in a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Bring next digit (7) of the dividend behind the 6 and repeat the process: 67 / 27

On to step 2:
The number 27 fits into 67 2 times, leaving a remainder of 13.
The next digit of our result is 2. 
Result so far: 2.0
The remainder is 13 after subtracting 54 from 67.
Append the next digit (9) from the dividend to 13 and continue with: 139 / 27

Moving on to step 3:
The number 27 fits into 139 5 times, leaving a remainder of 4.
Write down 5 as next digit of the result. 
Result so far: 25.0
The remainder is 4 after subtracting 135 from 139.
Bring next digit (1) of the dividend behind the 4 and repeat the process: 41 / 27

Advancing to step 4:
27 goes into 41 1 times with a remainder of 14.
Record the quotient 1 as the next digit in the result. 
Result so far: 251.0
The remainder is 14 after subtracting 27 from 41.
Grab the next digit (2) from the dividend, add it to 14, then carry on: 142 / 27

On to step 5:
When dividing 142 by 27, we get 5 with a remainder of 7.
Record the quotient 5 as the next digit in the result. 
Result so far: 2515.0
Deduct 135 from 142 and we're left with 7.
Append the next digit (5) from the dividend to 7 and continue with: 75 / 27

Step 6:
If we divide 75 by 27, we get 2 and a remainder of 21.
Put 2 as the next digit of the answer. 
Result so far: 25152.0
If we take 54 away from 75, we end up with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Moving on to step 7:
The number 27 fits into 210 7 times, leaving a remainder of 21.
The number 7 becomes the next digit in our result. 
Result so far: 25152.7
If we subtract 189 from 210, we get 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Let's proceed to step 8:
27 can be fit into 210 7 times, resulting in a remainder of 21.
Use 7 as the next digit of our solution. 
Result so far: 25152.77
If we take 189 away from 210, we end up with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

In conclusion, the division gives 25152.77 with a balance of 0.021.