We look at the division of 309005 by 34 
We're looking to find how many times 34 goes into 309005.

Step 1:
3 divided by 34 is 0 with a remainder of 3.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 3 to get 3.
Fetch the next digit (0) from the dividend, attach it to 3 and continue: 30 / 34

On to step 2:
When dividing 30 by 34, we get 0 with a remainder of 30.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 30 to get 30.
Include the next digit (9) from the dividend after 30, then repeat: 309 / 34

Moving on to step 3:
34 goes into 309 9 times with a remainder of 3.
The next digit of our result is 9. 
Result so far: 9.0
If we subtract 306 from 309, we get 3.
Append the next digit (0) from the dividend to 3 and continue with: 30 / 34

Going ahead to step 4:
The number 34 fits into 30 0 times, leaving a remainder of 30.
Use 0 as the next digit of our solution. 
Result so far: 90.0
Deduct 0 from 30 and we're left with 30.
Grab the next digit (0) from the dividend, add it to 30, then carry on: 300 / 34

Going ahead to step 5:
If we divide 300 by 34, we get 8 and a remainder of 28.
The next digit of our result is 8. 
Result so far: 908.0
Subtracting 272 from 300 leaves us with 28.
Append the next digit (5) from the dividend to 28 and continue with: 285 / 34

Step 6:
When dividing 285 by 34, we get 8 with a remainder of 13.
Use 8 as the next digit of our solution. 
Result so far: 9088.0
If we subtract 272 from 285, we get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

On to step 7:
34 can be fit into 130 3 times, resulting in a remainder of 28.
The next digit of our result is 3. 
Result so far: 9088.3
If we subtract 102 from 130, we get 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

On to step 8:
The number 34 fits into 280 8 times, leaving a remainder of 8.
Record the quotient 8 as the next digit in the result. 
Result so far: 9088.38
If we subtract 272 from 280, we get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Let's proceed to step 9:
If we divide 80 by 34, we get 2 and a remainder of 12.
Write down 2 as next digit of the result. 
Result so far: 9088.382
Subtracting 68 from 80 leaves us with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Advancing to step 10:
The number 34 fits into 120 3 times, leaving a remainder of 18.
Put 3 as the next digit of the answer. 
Result so far: 9088.3823
If we take 102 away from 120, we end up with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Advancing to step 11:
180 divided by 34 is 5 with a remainder of 10.
Record the quotient 5 as the next digit in the result. 
Result so far: 9088.38235
If we take 170 away from 180, we end up 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 12:
34 can be fit into 100 2 times, resulting in a remainder of 32.
Record the quotient 2 as the next digit in the result. 
Result so far: 9088.382352
Deduct 68 from 100 and we're left with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Let's proceed to step 13:
If we divide 320 by 34, we get 9 and a remainder of 14.
The number 9 becomes the next digit in our result. 
Result so far: 9088.3823529
If we subtract 306 from 320, we get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Moving on to step 14:
140 divided by 34 is 4 with a remainder of 4.
Put 4 as the next digit of the answer. 
Result so far: 9088.38235294
Deduct 136 from 140 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.

In conclusion, the division gives 9088.38235294 with a balance of 4e-09.