We're dividing 603 by 35 
Our goal is to divide 603 by 35.

Advancing to step 1:
35 goes into 6 0 times with a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 6 after subtracting 0 from 6.
Include the next digit (0) from the dividend after 6, then repeat: 60 / 35

Step 2:
60 divided by 35 is 1 with a remainder of 25.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Subtract 35 from 60 to get 25.
Fetch the next digit (3) from the dividend, attach it to 25 and continue: 253 / 35

Going ahead to step 3:
If we divide 253 by 35, we get 7 and a remainder of 8.
Use 7 as the next digit of our solution. 
Result so far: 17.0
Deduct 245 from 253 and we're left with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

On to step 4:
35 can be fit into 80 2 times, resulting in a remainder of 10.
Record the quotient 2 as the next digit in the result. 
Result so far: 17.2
Subtract 70 from 80 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Going ahead to step 5:
35 can be fit into 100 2 times, resulting in a remainder of 30.
Put 2 as the next digit of the answer. 
Result so far: 17.22
If we take 70 away from 100, we end up with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

In conclusion, the division gives 17.22 with a balance of 0.03.