We divide 32003 by 3
Our goal is to divide 32003 by 3.

On to step 1:
When dividing 3 by 3, we get 1 with a remainder of 0.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Deduct 3 from 3 and we're left with 0.
Include the next digit (2) from the dividend after 0, then repeat: 2 / 3

Step 2:
When dividing 2 by 3, we get 0 with a remainder of 2.
The next digit of our result is 0. 
Result so far: 10.0
The remainder is 2 after subtracting 0 from 2.
Include the next digit (0) from the dividend after 2, then repeat: 20 / 3

Moving on to step 3:
20 divided by 3 is 6 with a remainder of 2.
Write down 6 as next digit of the result. 
Result so far: 106.0
Subtract 18 from 20 to get 2.
Fetch the next digit (0) from the dividend, attach it to 2 and continue: 20 / 3

Going ahead to step 4:
3 goes into 20 6 times with a remainder of 2.
The next digit of our result is 6. 
Result so far: 1066.0
Deduct 18 from 20 and we're left with 2.
Bring next digit (3) of the dividend behind the 2 and repeat the process: 23 / 3

Going ahead to step 5:
If we divide 23 by 3, we get 7 and a remainder of 2.
The number 7 becomes the next digit in our result. 
Result so far: 10667.0
Subtracting 21 from 23 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Advancing to step 6:
When dividing 20 by 3, we get 6 with a remainder of 2.
Write down 6 as next digit of the result. 
Result so far: 10667.6
Subtract 18 from 20 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 7:
When dividing 20 by 3, we get 6 with a remainder of 2.
The next digit of our result is 6. 
Result so far: 10667.66
Subtract 18 from 20 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

After the division, we end up with 10667.66 and a remainder of 0.002.