509166 ÷ 33 
Our goal is to divide 509166 by 33.

Moving on to step 1:
When dividing 5 by 33, we get 0 with 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.
Append the next digit (0) from the dividend to 5 and continue with: 50 / 33

On to step 2:
If we divide 50 by 33, we get 1 and a remainder of 17.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we take 33 away from 50, we end up with 17.
Grab the next digit (9) from the dividend, add it to 17, then carry on: 179 / 33

Advancing to step 3:
33 goes into 179 5 times with a remainder of 14.
Use 5 as the next digit of our solution. 
Result so far: 15.0
If we take 165 away from 179, we end up with 14.
Append the next digit (1) from the dividend to 14 and continue with: 141 / 33

Advancing to step 4:
If we divide 141 by 33, we get 4 and a remainder of 9.
The number 4 becomes the next digit in our result. 
Result so far: 154.0
Subtracting 132 from 141 leaves us with 9.
Take the next digit (6) from the dividend and append it to 9, then repeat: 96 / 33

Going ahead to step 5:
When dividing 96 by 33, we get 2 with a remainder of 30.
Record the quotient 2 as the next digit in the result. 
Result so far: 1542.0
Subtract 66 from 96 to get 30.
Bring next digit (6) of the dividend behind the 30 and repeat the process: 306 / 33

On to step 6:
The number 33 fits into 306 9 times, leaving a remainder of 9.
Put 9 as the next digit of the answer. 
Result so far: 15429.0
Deduct 297 from 306 and we're left with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Moving on to step 7:
The number 33 fits into 90 2 times, leaving a remainder of 24.
Write down 2 as next digit of the result. 
Result so far: 15429.2
Subtract 66 from 90 to get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Step 8:
240 divided by 33 is 7 with a remainder of 9.
The number 7 becomes the next digit in our result. 
Result so far: 15429.27
Subtracting 231 from 240 leaves us with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Going ahead to step 9:
When dividing 90 by 33, we get 2 with a remainder of 24.
The number 2 becomes the next digit in our result. 
Result so far: 15429.272
Subtract 66 from 90 to get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Step 10:
If we divide 240 by 33, we get 7 and a remainder of 9.
Put 7 as the next digit of the answer. 
Result so far: 15429.2727
Deduct 231 from 240 and we're left with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Step 11:
90 divided by 33 is 2 with a remainder of 24.
Write down 2 as next digit of the result. 
Result so far: 15429.27272
The remainder is 24 after subtracting 66 from 90.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Let's proceed to step 12:
33 can be fit into 240 7 times, resulting in a remainder of 9.
Use 7 as the next digit of our solution. 
Result so far: 15429.272727
If we take 231 away from 240, we end up with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

On to step 13:
90 divided by 33 is 2 with a remainder of 24.
Write down 2 as next digit of the result. 
Result so far: 15429.2727272
Deduct 66 from 90 and we're left 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.

Let's proceed to step 14:
240 divided by 33 is 7 with a remainder of 9.
Use 7 as the next digit of our solution. 
Result so far: 15429.27272727
Subtracting 231 from 240 leaves us with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

In conclusion, the division gives 15429.27272727 with a balance of 9e-09.