We're dividing 420782 by 96 
We're looking to find how many times 96 goes into 420782.

On to step 1:
When dividing 4 by 96, we get 0 with a remainder of 4.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 4 to get 4.
Take the next digit (2) from the dividend and append it to 4, then repeat: 42 / 96

Step 2:
When dividing 42 by 96, we get 0 with a remainder of 42.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 42 and we're left with 42.
Append the next digit (0) from the dividend to 42 and continue with: 420 / 96

Let's proceed to step 3:
When dividing 420 by 96, we get 4 with a remainder of 36.
The number 4 becomes the next digit in our result. 
Result so far: 4.0
If we take 384 away from 420, we end up with 36.
Append the next digit (7) from the dividend to 36 and continue with: 367 / 96

Moving on to step 4:
367 divided by 96 is 3 with a remainder of 79.
The next digit of our result is 3. 
Result so far: 43.0
If we subtract 288 from 367, we get 79.
Include the next digit (8) from the dividend after 79, then repeat: 798 / 96

On to step 5:
If we divide 798 by 96, we get 8 and a remainder of 30.
Put 8 as the next digit of the answer. 
Result so far: 438.0
Subtracting 768 from 798 leaves us with 30.
Fetch the next digit (2) from the dividend, attach it to 30 and continue: 302 / 96

Step 6:
The number 96 fits into 302 3 times, leaving a remainder of 14.
Record the quotient 3 as the next digit in the result. 
Result so far: 4383.0
The remainder is 14 after subtracting 288 from 302.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

On to step 7:
96 can be fit into 140 1 times, resulting in a remainder of 44.
Put 1 as the next digit of the answer. 
Result so far: 4383.1
If we subtract 96 from 140, we get 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

On to step 8:
When dividing 440 by 96, we get 4 with a remainder of 56.
Use 4 as the next digit of our solution. 
Result so far: 4383.14
Subtract 384 from 440 to get 56.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

Going ahead to step 9:
560 divided by 96 is 5 with a remainder of 80.
Use 5 as the next digit of our solution. 
Result so far: 4383.145
The remainder is 80 after subtracting 480 from 560.
Since there are no more digits in the dividend, we add a zero to the remainder making it 800, and continue the process.

Let's proceed to step 10:
The number 96 fits into 800 8 times, leaving a remainder of 32.
The number 8 becomes the next digit in our result. 
Result so far: 4383.1458
Subtracting 768 from 800 leaves us with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Moving on to step 11:
96 goes into 320 3 times with a remainder of 32.
The number 3 becomes the next digit in our result. 
Result so far: 4383.14583
Subtracting 288 from 320 leaves us with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Moving on to step 12:
96 goes into 320 3 times with a remainder of 32.
Write down 3 as next digit of the result. 
Result so far: 4383.145833
If we subtract 288 from 320, we get 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

In conclusion, the division gives 4383.145833 with a balance of 3.2e-06.