34541 ÷ 81 
Our goal is to divide 34541 by 81.

Moving on to step 1:
If we divide 3 by 81, we get 0 and a remainder of 3.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 3 leaves us with 3.
Append the next digit (4) from the dividend to 3 and continue with: 34 / 81

Going ahead to step 2:
The number 81 fits into 34 0 times, leaving a remainder of 34.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 34 to get 34.
Grab the next digit (5) from the dividend, add it to 34, then carry on: 345 / 81

Step 3:
345 divided by 81 is 4 with a remainder of 21.
The number 4 becomes the next digit in our result. 
Result so far: 4.0
If we subtract 324 from 345, we get 21.
Append the next digit (4) from the dividend to 21 and continue with: 214 / 81

Step 4:
214 divided by 81 is 2 with a remainder of 52.
The next digit of our result is 2. 
Result so far: 42.0
Deduct 162 from 214 and we're left with 52.
Fetch the next digit (1) from the dividend, attach it to 52 and continue: 521 / 81

On to step 5:
81 goes into 521 6 times with a remainder of 35.
The next digit of our result is 6. 
Result so far: 426.0
Deduct 486 from 521 and we're left with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Step 6:
When dividing 350 by 81, we get 4 with a remainder of 26.
Use 4 as the next digit of our solution. 
Result so far: 426.4
If we subtract 324 from 350, we get 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Advancing to step 7:
81 goes into 260 3 times with a remainder of 17.
The next digit of our result is 3. 
Result so far: 426.43
Subtract 243 from 260 to get 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Let's proceed to step 8:
If we divide 170 by 81, we get 2 and a remainder of 8.
The next digit of our result is 2. 
Result so far: 426.432
If we subtract 162 from 170, we get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Going ahead to step 9:
81 can be fit into 80 0 times, resulting in a remainder of 80.
Write down 0 as next digit of the result. 
Result so far: 426.432
Subtracting 0 from 80 leaves us with 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 800, and continue the process.

Step 10:
The number 81 fits into 800 9 times, leaving a remainder of 71.
Record the quotient 9 as the next digit in the result. 
Result so far: 426.43209
The remainder is 71 after subtracting 729 from 800.
Since there are no more digits in the dividend, we add a zero to the remainder making it 710, and continue the process.

Going ahead to step 11:
710 divided by 81 is 8 with a remainder of 62.
Put 8 as the next digit of the answer. 
Result so far: 426.432098
Subtracting 648 from 710 leaves us with 62.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

Let's proceed to step 12:
When dividing 620 by 81, we get 7 with a remainder of 53.
Use 7 as the next digit of our solution. 
Result so far: 426.4320987
Subtracting 567 from 620 leaves us with 53.
Since there are no more digits in the dividend, we add a zero to the remainder making it 530, and continue the process.

Moving on to step 13:
81 goes into 530 6 times with a remainder of 44.
Use 6 as the next digit of our solution. 
Result so far: 426.43209876
Deduct 486 from 530 and we're left with 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

In conclusion, the division gives 426.43209876 with a balance of 4.4e-08.