We're dividing 359003 by 3 
We want to divide 359003 by 3.

Advancing to step 1:
When dividing 3 by 3, we get 1 with a remainder of 0.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we subtract 3 from 3, we get 0.
Fetch the next digit (5) from the dividend, attach it to 0 and continue: 5 / 3

On to step 2:
3 goes into 5 1 times with a remainder of 2.
Put 1 as the next digit of the answer. 
Result so far: 11.0
Subtract 3 from 5 to get 2.
Grab the next digit (9) from the dividend, add it to 2, then carry on: 29 / 3

Advancing to step 3:
When dividing 29 by 3, we get 9 with a remainder of 2.
Record the quotient 9 as the next digit in the result. 
Result so far: 119.0
If we take 27 away from 29, we end up with 2.
Append the next digit (0) from the dividend to 2 and continue with: 20 / 3

Advancing to step 4:
3 goes into 20 6 times with a remainder of 2.
Use 6 as the next digit of our solution. 
Result so far: 1196.0
If we subtract 18 from 20, we get 2.
Take the next digit (0) from the dividend and append it to 2, then repeat: 20 / 3

Advancing to step 5:
If we divide 20 by 3, we get 6 and a remainder of 2.
The number 6 becomes the next digit in our result. 
Result so far: 11966.0
If we take 18 away from 20, we end up with 2.
Include the next digit (3) from the dividend after 2, then repeat: 23 / 3

Advancing to step 6:
When dividing 23 by 3, we get 7 with a remainder of 2.
Write down 7 as next digit of the result. 
Result so far: 119667.0
If we take 21 away from 23, we end up 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.

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: 119667.6
If we subtract 18 from 20, we 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.

Advancing to step 8:
3 can be fit into 20 6 times, resulting in a remainder of 2.
Write down 6 as next digit of the result. 
Result so far: 119667.66
Subtracting 18 from 20 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.

The final outcome is 119667.66, with a leftover of 0.002.