510612 ÷ 9 
Let's see how many times 9 fits into 510612.

Going ahead to step 1:
If we divide 5 by 9, we get 0 and 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.
Take the next digit (1) from the dividend and append it to 5, then repeat: 51 / 9

Advancing to step 2:
9 can be fit into 51 5 times, resulting in a remainder of 6.
Record the quotient 5 as the next digit in the result. 
Result so far: 5.0
The remainder is 6 after subtracting 45 from 51.
Include the next digit (0) from the dividend after 6, then repeat: 60 / 9

Moving on to step 3:
If we divide 60 by 9, we get 6 and a remainder of 6.
The next digit of our result is 6. 
Result so far: 56.0
If we take 54 away from 60, we end up with 6.
Include the next digit (6) from the dividend after 6, then repeat: 66 / 9

Let's proceed to step 4:
If we divide 66 by 9, we get 7 and a remainder of 3.
Record the quotient 7 as the next digit in the result. 
Result so far: 567.0
If we take 63 away from 66, we end up with 3.
Fetch the next digit (1) from the dividend, attach it to 3 and continue: 31 / 9

On to step 5:
The number 9 fits into 31 3 times, leaving a remainder of 4.
Record the quotient 3 as the next digit in the result. 
Result so far: 5673.0
Subtract 27 from 31 to get 4.
Bring next digit (2) of the dividend behind the 4 and repeat the process: 42 / 9

Step 6:
The number 9 fits into 42 4 times, leaving a remainder of 6.
Use 4 as the next digit of our solution. 
Result so far: 56734.0
Deduct 36 from 42 and we're left 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.

On to step 7:
9 can be fit into 60 6 times, resulting in a remainder of 6.
Use 6 as the next digit of our solution. 
Result so far: 56734.6
If we subtract 54 from 60, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Advancing to step 8:
When dividing 60 by 9, we get 6 with a remainder of 6.
Put 6 as the next digit of the answer. 
Result so far: 56734.66
Deduct 54 from 60 and we're left 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.

After the division, we end up with 56734.66 and a remainder of 0.006.