Let's divide 684565 by 81
We want to divide 684565 by 81.

Moving on to step 1:
6 divided by 81 is 0 with a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 6 and we're left with 6.
Append the next digit (8) from the dividend to 6 and continue with: 68 / 81

Step 2:
81 can be fit into 68 0 times, resulting in a remainder of 68.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 68, we get 68.
Fetch the next digit (4) from the dividend, attach it to 68 and continue: 684 / 81

Going ahead to step 3:
81 can be fit into 684 8 times, resulting in a remainder of 36.
Write down 8 as next digit of the result. 
Result so far: 8.0
The remainder is 36 after subtracting 648 from 684.
Bring next digit (5) of the dividend behind the 36 and repeat the process: 365 / 81

Moving on to step 4:
When dividing 365 by 81, we get 4 with a remainder of 41.
Write down 4 as next digit of the result. 
Result so far: 84.0
The remainder is 41 after subtracting 324 from 365.
Bring next digit (6) of the dividend behind the 41 and repeat the process: 416 / 81

Advancing to step 5:
81 can be fit into 416 5 times, resulting in a remainder of 11.
The next digit of our result is 5. 
Result so far: 845.0
If we take 405 away from 416, we end up with 11.
Append the next digit (5) from the dividend to 11 and continue with: 115 / 81

Moving on to step 6:
81 can be fit into 115 1 times, resulting in a remainder of 34.
Use 1 as the next digit of our solution. 
Result so far: 8451.0
Subtracting 81 from 115 leaves us with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Let's proceed to step 7:
340 divided by 81 is 4 with a remainder of 16.
The next digit of our result is 4. 
Result so far: 8451.4
Subtracting 324 from 340 leaves us with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Advancing to step 8:
If we divide 160 by 81, we get 1 and a remainder of 79.
The number 1 becomes the next digit in our result. 
Result so far: 8451.41
If we subtract 81 from 160, we get 79.
Since there are no more digits in the dividend, we add a zero to the remainder making it 790, and continue the process.

Going ahead to step 9:
81 can be fit into 790 9 times, resulting in a remainder of 61.
Use 9 as the next digit of our solution. 
Result so far: 8451.419
If we subtract 729 from 790, we get 61.
Since there are no more digits in the dividend, we add a zero to the remainder making it 610, and continue the process.

Step 10:
If we divide 610 by 81, we get 7 and a remainder of 43.
Write down 7 as next digit of the result. 
Result so far: 8451.4197
Subtract 567 from 610 to get 43.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

Going ahead to step 11:
81 goes into 430 5 times with a remainder of 25.
Write down 5 as next digit of the result. 
Result so far: 8451.41975
Subtract 405 from 430 to get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

On to step 12:
81 goes into 250 3 times with a remainder of 7.
Record the quotient 3 as the next digit in the result. 
Result so far: 8451.419753
Deduct 243 from 250 and we're left with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Advancing to step 13:
81 can be fit into 70 0 times, resulting in a remainder of 70.
Use 0 as the next digit of our solution. 
Result so far: 8451.419753
Subtract 0 from 70 to get 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Moving on to step 14:
700 divided by 81 is 8 with a remainder of 52.
Record the quotient 8 as the next digit in the result. 
Result so far: 8451.41975308
Deduct 648 from 700 and we're left with 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

The final result is 8451.41975308 with a remainder of 5.2e-08.