We're dividing 510586 by 66 
Let's see how many times 66 fits into 510586.

Step 1:
The number 66 fits into 5 0 times, leaving a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Grab the next digit (1) from the dividend, add it to 5, then carry on: 51 / 66

Advancing to step 2:
If we divide 51 by 66, we get 0 and a remainder of 51.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 51 after subtracting 0 from 51.
Take the next digit (0) from the dividend and append it to 51, then repeat: 510 / 66

Step 3:
If we divide 510 by 66, we get 7 and a remainder of 48.
Record the quotient 7 as the next digit in the result. 
Result so far: 7.0
Subtracting 462 from 510 leaves us with 48.
Include the next digit (5) from the dividend after 48, then repeat: 485 / 66

Moving on to step 4:
If we divide 485 by 66, we get 7 and a remainder of 23.
Write down 7 as next digit of the result. 
Result so far: 77.0
Subtracting 462 from 485 leaves us with 23.
Take the next digit (8) from the dividend and append it to 23, then repeat: 238 / 66

On to step 5:
238 divided by 66 is 3 with a remainder of 40.
Use 3 as the next digit of our solution. 
Result so far: 773.0
Subtract 198 from 238 to get 40.
Include the next digit (6) from the dividend after 40, then repeat: 406 / 66

Going ahead to step 6:
406 divided by 66 is 6 with a remainder of 10.
Put 6 as the next digit of the answer. 
Result so far: 7736.0
Subtract 396 from 406 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 7:
When dividing 100 by 66, we get 1 with a remainder of 34.
Write down 1 as next digit of the result. 
Result so far: 7736.1
The remainder is 34 after subtracting 66 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Going ahead to step 8:
66 can be fit into 340 5 times, resulting in a remainder of 10.
The next digit of our result is 5. 
Result so far: 7736.15
Subtracting 330 from 340 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.

Advancing to step 9:
100 divided by 66 is 1 with a remainder of 34.
Put 1 as the next digit of the answer. 
Result so far: 7736.151
The remainder is 34 after subtracting 66 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Moving on to step 10:
66 goes into 340 5 times with a remainder of 10.
The number 5 becomes the next digit in our result. 
Result so far: 7736.1515
The remainder is 10 after subtracting 330 from 340.
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 11:
The number 66 fits into 100 1 times, leaving a remainder of 34.
The number 1 becomes the next digit in our result. 
Result so far: 7736.15151
If we take 66 away from 100, we end up with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

On to step 12:
If we divide 340 by 66, we get 5 and a remainder of 10.
The next digit of our result is 5. 
Result so far: 7736.151515
Subtracting 330 from 340 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.

Let's proceed to step 13:
66 can be fit into 100 1 times, resulting in a remainder of 34.
Use 1 as the next digit of our solution. 
Result so far: 7736.1515151
If we subtract 66 from 100, we get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Moving on to step 14:
If we divide 340 by 66, we get 5 and a remainder of 10.
The next digit of our result is 5. 
Result so far: 7736.15151515
If we subtract 330 from 340, we 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.

In conclusion, the division gives 7736.15151515 with a balance of 1e-08.