We look at the division of 541666 by 81 
We're looking to find how many times 81 goes into 541666.

Going ahead to step 1:
81 goes into 5 0 times with a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Include the next digit (4) from the dividend after 5, then repeat: 54 / 81

On to step 2:
When dividing 54 by 81, we get 0 with a remainder of 54.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 54 to get 54.
Bring next digit (1) of the dividend behind the 54 and repeat the process: 541 / 81

Let's proceed to step 3:
The number 81 fits into 541 6 times, leaving a remainder of 55.
Record the quotient 6 as the next digit in the result. 
Result so far: 6.0
Subtract 486 from 541 to get 55.
Fetch the next digit (6) from the dividend, attach it to 55 and continue: 556 / 81

Let's proceed to step 4:
81 goes into 556 6 times with a remainder of 70.
The next digit of our result is 6. 
Result so far: 66.0
If we subtract 486 from 556, we get 70.
Bring next digit (6) of the dividend behind the 70 and repeat the process: 706 / 81

Let's proceed to step 5:
If we divide 706 by 81, we get 8 and a remainder of 58.
Write down 8 as next digit of the result. 
Result so far: 668.0
Subtracting 648 from 706 leaves us with 58.
Append the next digit (6) from the dividend to 58 and continue with: 586 / 81

Advancing to step 6:
When dividing 586 by 81, we get 7 with a remainder of 19.
Record the quotient 7 as the next digit in the result. 
Result so far: 6687.0
The remainder is 19 after subtracting 567 from 586.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Moving on to step 7:
81 can be fit into 190 2 times, resulting in a remainder of 28.
The next digit of our result is 2. 
Result so far: 6687.2
If we take 162 away from 190, we end up 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.

Let's proceed to step 8:
If we divide 280 by 81, we get 3 and a remainder of 37.
The next digit of our result is 3. 
Result so far: 6687.23
The remainder is 37 after subtracting 243 from 280.
Since there are no more digits in the dividend, we add a zero to the remainder making it 370, and continue the process.

Going ahead to step 9:
81 can be fit into 370 4 times, resulting in a remainder of 46.
Use 4 as the next digit of our solution. 
Result so far: 6687.234
The remainder is 46 after subtracting 324 from 370.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

On to step 10:
460 divided by 81 is 5 with a remainder of 55.
The next digit of our result is 5. 
Result so far: 6687.2345
If we subtract 405 from 460, 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.

Step 11:
When dividing 550 by 81, we get 6 with a remainder of 64.
Use 6 as the next digit of our solution. 
Result so far: 6687.23456
The remainder is 64 after subtracting 486 from 550.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

Moving on to step 12:
When dividing 640 by 81, we get 7 with a remainder of 73.
The next digit of our result is 7. 
Result so far: 6687.234567
Subtract 567 from 640 to get 73.
Since there are no more digits in the dividend, we add a zero to the remainder making it 730, and continue the process.

Advancing to step 13:
730 divided by 81 is 9 with a remainder of 1.
Use 9 as the next digit of our solution. 
Result so far: 6687.2345679
Deduct 729 from 730 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Moving on to step 14:
If we divide 10 by 81, we get 0 and a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 6687.2345679
Deduct 0 from 10 and we're left with 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 6687.2345679 with a balance of 1e-08.