Let's divide 509318 by 34
We're looking to find how many times 34 goes into 509318.

Going ahead to step 1:
5 divided by 34 is 0 with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Include the next digit (0) from the dividend after 5, then repeat: 50 / 34

Moving on to step 2:
If we divide 50 by 34, we get 1 and a remainder of 16.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Subtract 34 from 50 to get 16.
Append the next digit (9) from the dividend to 16 and continue with: 169 / 34

Advancing to step 3:
If we divide 169 by 34, we get 4 and a remainder of 33.
The number 4 becomes the next digit in our result. 
Result so far: 14.0
Subtracting 136 from 169 leaves us with 33.
Bring next digit (3) of the dividend behind the 33 and repeat the process: 333 / 34

Going ahead to step 4:
333 divided by 34 is 9 with a remainder of 27.
The number 9 becomes the next digit in our result. 
Result so far: 149.0
Deduct 306 from 333 and we're left with 27.
Grab the next digit (1) from the dividend, add it to 27, then carry on: 271 / 34

On to step 5:
34 can be fit into 271 7 times, resulting in a remainder of 33.
Put 7 as the next digit of the answer. 
Result so far: 1497.0
Subtracting 238 from 271 leaves us with 33.
Bring next digit (8) of the dividend behind the 33 and repeat the process: 338 / 34

Step 6:
34 goes into 338 9 times with a remainder of 32.
Record the quotient 9 as the next digit in the result. 
Result so far: 14979.0
Subtract 306 from 338 to 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.

Moving on to step 7:
34 goes into 320 9 times with a remainder of 14.
Record the quotient 9 as the next digit in the result. 
Result so far: 14979.9
Subtracting 306 from 320 leaves us with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

On to step 8:
If we divide 140 by 34, we get 4 and a remainder of 4.
The number 4 becomes the next digit in our result. 
Result so far: 14979.94
The remainder is 4 after subtracting 136 from 140.
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 9:
The number 34 fits into 40 1 times, leaving a remainder of 6.
The number 1 becomes the next digit in our result. 
Result so far: 14979.941
Subtracting 34 from 40 leaves us with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 10:
34 can be fit into 60 1 times, resulting in a remainder of 26.
Record the quotient 1 as the next digit in the result. 
Result so far: 14979.9411
Deduct 34 from 60 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.

In conclusion, the division gives 14979.9411 with a balance of 0.00026.