510599 ÷ 9 
Let's see how many times 9 fits into 510599.

Let's proceed to step 1:
When dividing 5 by 9, we get 0 with a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Bring next digit (1) of the dividend behind the 5 and repeat the process: 51 / 9

Moving on to step 2:
9 goes into 51 5 times with a remainder of 6.
Write down 5 as next digit of the result. 
Result so far: 5.0
Subtracting 45 from 51 leaves us with 6.
Fetch the next digit (0) from the dividend, attach it to 6 and continue: 60 / 9

On to step 3:
If we divide 60 by 9, we get 6 and a remainder of 6.
Record the quotient 6 as the next digit in the result. 
Result so far: 56.0
Subtracting 54 from 60 leaves us with 6.
Append the next digit (5) from the dividend to 6 and continue with: 65 / 9

Going ahead to step 4:
9 can be fit into 65 7 times, resulting in a remainder of 2.
Put 7 as the next digit of the answer. 
Result so far: 567.0
The remainder is 2 after subtracting 63 from 65.
Include the next digit (9) from the dividend after 2, then repeat: 29 / 9

Advancing to step 5:
The number 9 fits into 29 3 times, leaving a remainder of 2.
Put 3 as the next digit of the answer. 
Result so far: 5673.0
Subtract 27 from 29 to get 2.
Fetch the next digit (9) from the dividend, attach it to 2 and continue: 29 / 9

Going ahead to step 6:
9 goes into 29 3 times with a remainder of 2.
The number 3 becomes the next digit in our result. 
Result so far: 56733.0
The remainder is 2 after subtracting 27 from 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Advancing to step 7:
9 goes into 20 2 times with a remainder of 2.
The number 2 becomes the next digit in our result. 
Result so far: 56733.2
Subtracting 18 from 20 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 8:
When dividing 20 by 9, we get 2 with a remainder of 2.
Record the quotient 2 as the next digit in the result. 
Result so far: 56733.22
Subtracting 18 from 20 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

In conclusion, the division gives 56733.22 with a balance of 0.002.