8541 ÷ 87 
We want to divide 8541 by 87.

Let's proceed to step 1:
If we divide 8 by 87, we get 0 and a remainder of 8.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 8 leaves us with 8.
Grab the next digit (5) from the dividend, add it to 8, then carry on: 85 / 87

Step 2:
87 goes into 85 0 times with a remainder of 85.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 85 and we're left with 85.
Fetch the next digit (4) from the dividend, attach it to 85 and continue: 854 / 87

On to step 3:
854 divided by 87 is 9 with a remainder of 71.
Use 9 as the next digit of our solution. 
Result so far: 9.0
Deduct 783 from 854 and we're left with 71.
Take the next digit (1) from the dividend and append it to 71, then repeat: 711 / 87

Step 4:
87 can be fit into 711 8 times, resulting in a remainder of 15.
Use 8 as the next digit of our solution. 
Result so far: 98.0
If we take 696 away from 711, we end up with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Advancing to step 5:
87 can be fit into 150 1 times, resulting in a remainder of 63.
Put 1 as the next digit of the answer. 
Result so far: 98.1
Subtract 87 from 150 to get 63.
Since there are no more digits in the dividend, we add a zero to the remainder making it 630, and continue the process.

Moving on to step 6:
If we divide 630 by 87, we get 7 and a remainder of 21.
Write down 7 as next digit of the result. 
Result so far: 98.17
The remainder is 21 after subtracting 609 from 630.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Going ahead to step 7:
If we divide 210 by 87, we get 2 and a remainder of 36.
Put 2 as the next digit of the answer. 
Result so far: 98.172
The remainder is 36 after subtracting 174 from 210.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Let's proceed to step 8:
360 divided by 87 is 4 with a remainder of 12.
The number 4 becomes the next digit in our result. 
Result so far: 98.1724
If we subtract 348 from 360, we get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Moving on to step 9:
87 goes into 120 1 times with a remainder of 33.
Record the quotient 1 as the next digit in the result. 
Result so far: 98.17241
If we subtract 87 from 120, we get 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Step 10:
When dividing 330 by 87, we get 3 with a remainder of 69.
The next digit of our result is 3. 
Result so far: 98.172413
If we take 261 away from 330, we end up with 69.
Since there are no more digits in the dividend, we add a zero to the remainder making it 690, and continue the process.

Step 11:
The number 87 fits into 690 7 times, leaving a remainder of 81.
Use 7 as the next digit of our solution. 
Result so far: 98.1724137
If we take 609 away from 690, we end up with 81.
Since there are no more digits in the dividend, we add a zero to the remainder making it 810, and continue the process.

Let's proceed to step 12:
When dividing 810 by 87, we get 9 with a remainder of 27.
The next digit of our result is 9. 
Result so far: 98.17241379
If we take 783 away from 810, we end up with 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Our division results in 98.17241379 with a remaining 2.7e-08.