We divide 756721 by 81
Our goal is to divide 756721 by 81.

Advancing to step 1:
When dividing 7 by 81, we get 0 with a remainder of 7.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 7 and we're left with 7.
Include the next digit (5) from the dividend after 7, then repeat: 75 / 81

Moving on to step 2:
If we divide 75 by 81, we get 0 and a remainder of 75.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 75 after subtracting 0 from 75.
Include the next digit (6) from the dividend after 75, then repeat: 756 / 81

Let's proceed to step 3:
If we divide 756 by 81, we get 9 and a remainder of 27.
The next digit of our result is 9. 
Result so far: 9.0
The remainder is 27 after subtracting 729 from 756.
Take the next digit (7) from the dividend and append it to 27, then repeat: 277 / 81

On to step 4:
When dividing 277 by 81, we get 3 with a remainder of 34.
The next digit of our result is 3. 
Result so far: 93.0
Subtracting 243 from 277 leaves us with 34.
Append the next digit (2) from the dividend to 34 and continue with: 342 / 81

Advancing to step 5:
The number 81 fits into 342 4 times, leaving a remainder of 18.
Put 4 as the next digit of the answer. 
Result so far: 934.0
The remainder is 18 after subtracting 324 from 342.
Include the next digit (1) from the dividend after 18, then repeat: 181 / 81

Advancing to step 6:
81 can be fit into 181 2 times, resulting in a remainder of 19.
Use 2 as the next digit of our solution. 
Result so far: 9342.0
The remainder is 19 after subtracting 162 from 181.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Going ahead to step 7:
190 divided by 81 is 2 with a remainder of 28.
Put 2 as the next digit of the answer. 
Result so far: 9342.2
Deduct 162 from 190 and we're left with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Advancing to step 8:
81 goes into 280 3 times with a remainder of 37.
The next digit of our result is 3. 
Result so far: 9342.23
If we subtract 243 from 280, we get 37.
Since there are no more digits in the dividend, we add a zero to the remainder making it 370, and continue the process.

Advancing to step 9:
The number 81 fits into 370 4 times, leaving a remainder of 46.
The next digit of our result is 4. 
Result so far: 9342.234
If we subtract 324 from 370, we get 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Moving on to step 10:
81 goes into 460 5 times with a remainder of 55.
Use 5 as the next digit of our solution. 
Result so far: 9342.2345
If we take 405 away from 460, we end up with 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Advancing to step 11:
When dividing 550 by 81, we get 6 with a remainder of 64.
The number 6 becomes the next digit in our result. 
Result so far: 9342.23456
If we subtract 486 from 550, we get 64.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

Going ahead to step 12:
81 goes into 640 7 times with a remainder of 73.
Record the quotient 7 as the next digit in the result. 
Result so far: 9342.234567
The remainder is 73 after subtracting 567 from 640.
Since there are no more digits in the dividend, we add a zero to the remainder making it 730, and continue the process.

On to step 13:
81 can be fit into 730 9 times, resulting in a remainder of 1.
Use 9 as the next digit of our solution. 
Result so far: 9342.2345679
If we subtract 729 from 730, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Let's proceed to step 14:
81 goes into 10 0 times with a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 9342.2345679
Subtract 0 from 10 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

In conclusion, the division gives 9342.2345679 with a balance of 1e-08.