We look at the division of 509630 by 3 
We want to figure out the number of times 509630 can be divided by 3.

Moving on to step 1:
3 can be fit into 5 1 times, resulting in a remainder of 2.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
If we take 3 away from 5, we end up with 2.
Take the next digit (0) from the dividend and append it to 2, then repeat: 20 / 3

Going ahead to step 2:
When dividing 20 by 3, we get 6 with a remainder of 2.
The next digit of our result is 6. 
Result so far: 16.0
The remainder is 2 after subtracting 18 from 20.
Fetch the next digit (9) from the dividend, attach it to 2 and continue: 29 / 3

Advancing to step 3:
29 divided by 3 is 9 with a remainder of 2.
Record the quotient 9 as the next digit in the result. 
Result so far: 169.0
Deduct 27 from 29 and we're left with 2.
Append the next digit (6) from the dividend to 2 and continue with: 26 / 3

Going ahead to step 4:
26 divided by 3 is 8 with a remainder of 2.
Use 8 as the next digit of our solution. 
Result so far: 1698.0
Subtract 24 from 26 to get 2.
Include the next digit (3) from the dividend after 2, then repeat: 23 / 3

Step 5:
If we divide 23 by 3, we get 7 and a remainder of 2.
Use 7 as the next digit of our solution. 
Result so far: 16987.0
If we take 21 away from 23, we end up with 2.
Fetch the next digit (0) from the dividend, attach it to 2 and continue: 20 / 3

Going ahead to step 6:
20 divided by 3 is 6 with a remainder of 2.
The number 6 becomes the next digit in our result. 
Result so far: 169876.0
The remainder is 2 after subtracting 18 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 7:
If we divide 20 by 3, we get 6 and a remainder of 2.
Put 6 as the next digit of the answer. 
Result so far: 169876.6
Deduct 18 from 20 and we're left 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 8:
The number 3 fits into 20 6 times, leaving a remainder of 2.
The next digit of our result is 6. 
Result so far: 169876.66
The remainder is 2 after subtracting 18 from 20.
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 result is 169876.66 with a remainder of 0.002.