509983 ÷ 15 
Our goal is to divide 509983 by 15.

Let's proceed to step 1:
If we divide 5 by 15, we get 0 and a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Fetch the next digit (0) from the dividend, attach it to 5 and continue: 50 / 15

Let's proceed to step 2:
50 divided by 15 is 3 with a remainder of 5.
The next digit of our result is 3. 
Result so far: 3.0
Deduct 45 from 50 and we're left with 5.
Take the next digit (9) from the dividend and append it to 5, then repeat: 59 / 15

Step 3:
59 divided by 15 is 3 with a remainder of 14.
Use 3 as the next digit of our solution. 
Result so far: 33.0
Deduct 45 from 59 and we're left with 14.
Include the next digit (9) from the dividend after 14, then repeat: 149 / 15

Let's proceed to step 4:
The number 15 fits into 149 9 times, leaving a remainder of 14.
The number 9 becomes the next digit in our result. 
Result so far: 339.0
Subtract 135 from 149 to get 14.
Bring next digit (8) of the dividend behind the 14 and repeat the process: 148 / 15

Advancing to step 5:
15 goes into 148 9 times with a remainder of 13.
The next digit of our result is 9. 
Result so far: 3399.0
The remainder is 13 after subtracting 135 from 148.
Take the next digit (3) from the dividend and append it to 13, then repeat: 133 / 15

Advancing to step 6:
When dividing 133 by 15, we get 8 with a remainder of 13.
Use 8 as the next digit of our solution. 
Result so far: 33998.0
Deduct 120 from 133 and we're left with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Going ahead to step 7:
130 divided by 15 is 8 with a remainder of 10.
Record the quotient 8 as the next digit in the result. 
Result so far: 33998.8
Deduct 120 from 130 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 8:
The number 15 fits into 100 6 times, leaving a remainder of 10.
The next digit of our result is 6. 
Result so far: 33998.86
Deduct 90 from 100 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 9:
The number 15 fits into 100 6 times, leaving a remainder of 10.
The next digit of our result is 6. 
Result so far: 33998.866
Subtracting 90 from 100 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

The final outcome is 33998.866, with a leftover of 0.001.