We look at the division of 509302 by 6 
We're looking to find how many times 6 goes into 509302.

Moving on to step 1:
When dividing 5 by 6, we get 0 with a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Grab the next digit (0) from the dividend, add it to 5, then carry on: 50 / 6

Step 2:
The number 6 fits into 50 8 times, leaving a remainder of 2.
The number 8 becomes the next digit in our result. 
Result so far: 8.0
Subtracting 48 from 50 leaves us with 2.
Take the next digit (9) from the dividend and append it to 2, then repeat: 29 / 6

Let's proceed to step 3:
If we divide 29 by 6, we get 4 and a remainder of 5.
The number 4 becomes the next digit in our result. 
Result so far: 84.0
Subtract 24 from 29 to get 5.
Take the next digit (3) from the dividend and append it to 5, then repeat: 53 / 6

Advancing to step 4:
53 divided by 6 is 8 with a remainder of 5.
The next digit of our result is 8. 
Result so far: 848.0
Deduct 48 from 53 and we're left with 5.
Include the next digit (0) from the dividend after 5, then repeat: 50 / 6

On to step 5:
If we divide 50 by 6, we get 8 and a remainder of 2.
The number 8 becomes the next digit in our result. 
Result so far: 8488.0
Deduct 48 from 50 and we're left with 2.
Bring next digit (2) of the dividend behind the 2 and repeat the process: 22 / 6

Step 6:
6 goes into 22 3 times with a remainder of 4.
The number 3 becomes the next digit in our result. 
Result so far: 84883.0
If we take 18 away from 22, we end up with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Let's proceed to step 7:
6 goes into 40 6 times with a remainder of 4.
Write down 6 as next digit of the result. 
Result so far: 84883.6
If we subtract 36 from 40, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 8:
6 goes into 40 6 times with a remainder of 4.
Write down 6 as next digit of the result. 
Result so far: 84883.66
Deduct 36 from 40 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

The final result is 84883.66 with a remainder of 0.004.