We look at the division of 534581 by 96 
Our goal is to divide 534581 by 96.

On to step 1:
5 divided by 96 is 0 with a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Include the next digit (3) from the dividend after 5, then repeat: 53 / 96

Going ahead to step 2:
When dividing 53 by 96, we get 0 with a remainder of 53.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 53, we get 53.
Append the next digit (4) from the dividend to 53 and continue with: 534 / 96

On to step 3:
The number 96 fits into 534 5 times, leaving a remainder of 54.
Record the quotient 5 as the next digit in the result. 
Result so far: 5.0
Subtracting 480 from 534 leaves us with 54.
Take the next digit (5) from the dividend and append it to 54, then repeat: 545 / 96

Moving on to step 4:
96 goes into 545 5 times with a remainder of 65.
Use 5 as the next digit of our solution. 
Result so far: 55.0
If we take 480 away from 545, we end up with 65.
Fetch the next digit (8) from the dividend, attach it to 65 and continue: 658 / 96

Let's proceed to step 5:
The number 96 fits into 658 6 times, leaving a remainder of 82.
The next digit of our result is 6. 
Result so far: 556.0
Subtract 576 from 658 to get 82.
Grab the next digit (1) from the dividend, add it to 82, then carry on: 821 / 96

On to step 6:
96 can be fit into 821 8 times, resulting in a remainder of 53.
The number 8 becomes the next digit in our result. 
Result so far: 5568.0
The remainder is 53 after subtracting 768 from 821.
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 7:
96 goes into 530 5 times with a remainder of 50.
The next digit of our result is 5. 
Result so far: 5568.5
If we subtract 480 from 530, we get 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Let's proceed to step 8:
96 goes into 500 5 times with a remainder of 20.
Use 5 as the next digit of our solution. 
Result so far: 5568.55
If we subtract 480 from 500, we get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

The final outcome is 5568.55, with a leftover of 0.02.