We're dividing 436181 by 96 
We're looking to find how many times 96 goes into 436181.

Advancing to step 1:
96 can be fit into 4 0 times, resulting in a remainder of 4.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 4 to get 4.
Append the next digit (3) from the dividend to 4 and continue with: 43 / 96

Let's proceed to step 2:
When dividing 43 by 96, we get 0 with a remainder of 43.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 43 and we're left with 43.
Include the next digit (6) from the dividend after 43, then repeat: 436 / 96

Let's proceed to step 3:
436 divided by 96 is 4 with a remainder of 52.
The next digit of our result is 4. 
Result so far: 4.0
The remainder is 52 after subtracting 384 from 436.
Include the next digit (1) from the dividend after 52, then repeat: 521 / 96

Going ahead to step 4:
96 goes into 521 5 times with a remainder of 41.
The next digit of our result is 5. 
Result so far: 45.0
Deduct 480 from 521 and we're left with 41.
Grab the next digit (8) from the dividend, add it to 41, then carry on: 418 / 96

Advancing to step 5:
96 goes into 418 4 times with a remainder of 34.
Write down 4 as next digit of the result. 
Result so far: 454.0
Subtracting 384 from 418 leaves us with 34.
Grab the next digit (1) from the dividend, add it to 34, then carry on: 341 / 96

On to step 6:
The number 96 fits into 341 3 times, leaving a remainder of 53.
Use 3 as the next digit of our solution. 
Result so far: 4543.0
The remainder is 53 after subtracting 288 from 341.
Since there are no more digits in the dividend, we add a zero to the remainder making it 530, and continue the process.

Step 7:
When dividing 530 by 96, we get 5 with a remainder of 50.
Use 5 as the next digit of our solution. 
Result so far: 4543.5
Deduct 480 from 530 and we're left with 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Moving on to step 8:
If we divide 500 by 96, we get 5 and a remainder of 20.
Record the quotient 5 as the next digit in the result. 
Result so far: 4543.55
Subtracting 480 from 500 leaves us with 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 result is 4543.55 with a remainder of 0.02.