We're dividing 9003 by 35 
Our goal is to divide 9003 by 35.

Moving on to step 1:
If we divide 9 by 35, we get 0 and a remainder of 9.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 9 and we're left with 9.
Append the next digit (0) from the dividend to 9 and continue with: 90 / 35

Advancing to step 2:
When dividing 90 by 35, we get 2 with a remainder of 20.
The number 2 becomes the next digit in our result. 
Result so far: 2.0
Subtracting 70 from 90 leaves us with 20.
Grab the next digit (0) from the dividend, add it to 20, then carry on: 200 / 35

Advancing to step 3:
When dividing 200 by 35, we get 5 with a remainder of 25.
The number 5 becomes the next digit in our result. 
Result so far: 25.0
Subtracting 175 from 200 leaves us with 25.
Include the next digit (3) from the dividend after 25, then repeat: 253 / 35

Advancing to step 4:
35 can be fit into 253 7 times, resulting in a remainder of 8.
Write down 7 as next digit of the result. 
Result so far: 257.0
If we subtract 245 from 253, we get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Moving on to step 5:
35 goes into 80 2 times with a remainder of 10.
Put 2 as the next digit of the answer. 
Result so far: 257.2
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.

Moving on to step 6:
35 goes into 100 2 times with a remainder of 30.
The next digit of our result is 2. 
Result so far: 257.22
Deduct 70 from 100 and we're left 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.

After the division, we end up with 257.22 and a remainder of 0.03.