We look at the division of 338603 by 96 
Our goal is to divide 338603 by 96.

On to step 1:
If we divide 3 by 96, we get 0 and a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 3 to get 3.
Bring next digit (3) of the dividend behind the 3 and repeat the process: 33 / 96

Step 2:
33 divided by 96 is 0 with a remainder of 33.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 33, we end up with 33.
Bring next digit (8) of the dividend behind the 33 and repeat the process: 338 / 96

Going ahead to step 3:
96 goes into 338 3 times with a remainder of 50.
Put 3 as the next digit of the answer. 
Result so far: 3.0
If we take 288 away from 338, we end up with 50.
Fetch the next digit (6) from the dividend, attach it to 50 and continue: 506 / 96

Advancing to step 4:
96 goes into 506 5 times with a remainder of 26.
The next digit of our result is 5. 
Result so far: 35.0
Deduct 480 from 506 and we're left with 26.
Grab the next digit (0) from the dividend, add it to 26, then carry on: 260 / 96

Advancing to step 5:
The number 96 fits into 260 2 times, leaving a remainder of 68.
The next digit of our result is 2. 
Result so far: 352.0
Deduct 192 from 260 and we're left with 68.
Fetch the next digit (3) from the dividend, attach it to 68 and continue: 683 / 96

Going ahead to step 6:
When dividing 683 by 96, we get 7 with a remainder of 11.
Put 7 as the next digit of the answer. 
Result so far: 3527.0
If we subtract 672 from 683, we get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Going ahead to step 7:
When dividing 110 by 96, we get 1 with a remainder of 14.
Write down 1 as next digit of the result. 
Result so far: 3527.1
If we take 96 away from 110, we end up with 14.
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 8:
96 can be fit into 140 1 times, resulting in a remainder of 44.
Record the quotient 1 as the next digit in the result. 
Result so far: 3527.11
Subtracting 96 from 140 leaves us 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.

The final outcome is 3527.11, with a leftover of 0.044.