We divide 679 by 81
We want to divide 679 by 81.

On to step 1:
81 goes into 6 0 times with a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 6 after subtracting 0 from 6.
Take the next digit (7) from the dividend and append it to 6, then repeat: 67 / 81

Moving on to step 2:
When dividing 67 by 81, we get 0 with a remainder of 67.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 67, we get 67.
Grab the next digit (9) from the dividend, add it to 67, then carry on: 679 / 81

Let's proceed to step 3:
When dividing 679 by 81, we get 8 with a remainder of 31.
Write down 8 as next digit of the result. 
Result so far: 8.0
Subtract 648 from 679 to get 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

On to step 4:
310 divided by 81 is 3 with a remainder of 67.
Record the quotient 3 as the next digit in the result. 
Result so far: 8.3
Subtract 243 from 310 to get 67.
Since there are no more digits in the dividend, we add a zero to the remainder making it 670, and continue the process.

Advancing to step 5:
670 divided by 81 is 8 with a remainder of 22.
Record the quotient 8 as the next digit in the result. 
Result so far: 8.38
If we subtract 648 from 670, we get 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Going ahead to step 6:
The number 81 fits into 220 2 times, leaving a remainder of 58.
The number 2 becomes the next digit in our result. 
Result so far: 8.382
Deduct 162 from 220 and we're left with 58.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

Step 7:
81 can be fit into 580 7 times, resulting in a remainder of 13.
The next digit of our result is 7. 
Result so far: 8.3827
If we subtract 567 from 580, we get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Going ahead to step 8:
130 divided by 81 is 1 with a remainder of 49.
Use 1 as the next digit of our solution. 
Result so far: 8.38271
Subtract 81 from 130 to get 49.
Since there are no more digits in the dividend, we add a zero to the remainder making it 490, and continue the process.

On to step 9:
When dividing 490 by 81, we get 6 with a remainder of 4.
The number 6 becomes the next digit in our result. 
Result so far: 8.382716
If we subtract 486 from 490, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 10:
When dividing 40 by 81, we get 0 with a remainder of 40.
Write down 0 as next digit of the result. 
Result so far: 8.382716
If we subtract 0 from 40, we get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Let's proceed to step 11:
81 goes into 400 4 times with a remainder of 76.
Put 4 as the next digit of the answer. 
Result so far: 8.38271604
If we take 324 away from 400, we end up with 76.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

In conclusion, the division gives 8.38271604 with a balance of 7.6e-08.