We look at the division of 509340 by 38 
We want to divide 509340 by 38.

Step 1:
5 divided by 38 is 0 with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Fetch the next digit (0) from the dividend, attach it to 5 and continue: 50 / 38

Step 2:
50 divided by 38 is 1 with a remainder of 12.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtract 38 from 50 to get 12.
Take the next digit (9) from the dividend and append it to 12, then repeat: 129 / 38

Let's proceed to step 3:
129 divided by 38 is 3 with a remainder of 15.
Write down 3 as next digit of the result. 
Result so far: 13.0
Subtract 114 from 129 to get 15.
Append the next digit (3) from the dividend to 15 and continue with: 153 / 38

Advancing to step 4:
153 divided by 38 is 4 with a remainder of 1.
Record the quotient 4 as the next digit in the result. 
Result so far: 134.0
If we take 152 away from 153, we end up with 1.
Grab the next digit (4) from the dividend, add it to 1, then carry on: 14 / 38

Moving on to step 5:
38 can be fit into 14 0 times, resulting in a remainder of 14.
Write down 0 as next digit of the result. 
Result so far: 1340.0
If we take 0 away from 14, we end up with 14.
Grab the next digit (0) from the dividend, add it to 14, then carry on: 140 / 38

Moving on to step 6:
140 divided by 38 is 3 with a remainder of 26.
Put 3 as the next digit of the answer. 
Result so far: 13403.0
Deduct 114 from 140 and we're left with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Let's proceed to step 7:
If we divide 260 by 38, we get 6 and a remainder of 32.
Record the quotient 6 as the next digit in the result. 
Result so far: 13403.6
If we subtract 228 from 260, we get 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

On to step 8:
When dividing 320 by 38, we get 8 with a remainder of 16.
Write down 8 as next digit of the result. 
Result so far: 13403.68
Deduct 304 from 320 and we're left with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Step 9:
The number 38 fits into 160 4 times, leaving a remainder of 8.
The next digit of our result is 4. 
Result so far: 13403.684
The remainder is 8 after subtracting 152 from 160.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Step 10:
38 goes into 80 2 times with a remainder of 4.
Record the quotient 2 as the next digit in the result. 
Result so far: 13403.6842
The remainder is 4 after subtracting 76 from 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Advancing to step 11:
38 can be fit into 40 1 times, resulting in a remainder of 2.
Use 1 as the next digit of our solution. 
Result so far: 13403.68421
If we take 38 away from 40, 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.

Going ahead to step 12:
The number 38 fits into 20 0 times, leaving a remainder of 20.
The number 0 becomes the next digit in our result. 
Result so far: 13403.68421
If we take 0 away from 20, we end up with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Step 13:
If we divide 200 by 38, we get 5 and a remainder of 10.
The number 5 becomes the next digit in our result. 
Result so far: 13403.6842105
Subtract 190 from 200 to get 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 14:
The number 38 fits into 100 2 times, leaving a remainder of 24.
The number 2 becomes the next digit in our result. 
Result so far: 13403.68421052
Subtracting 76 from 100 leaves us with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

The final result is 13403.68421052 with a remainder of 2.4e-08.