506631 ÷ 9 
Our goal is to divide 506631 by 9.

Step 1:
When dividing 5 by 9, we get 0 with 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 (0) from the dividend and append it to 5, then repeat: 50 / 9

Advancing to step 2:
50 divided by 9 is 5 with a remainder of 5.
The next digit of our result is 5. 
Result so far: 5.0
If we take 45 away from 50, we end up with 5.
Fetch the next digit (6) from the dividend, attach it to 5 and continue: 56 / 9

Advancing to step 3:
The number 9 fits into 56 6 times, leaving a remainder of 2.
Record the quotient 6 as the next digit in the result. 
Result so far: 56.0
Subtracting 54 from 56 leaves us with 2.
Bring next digit (6) of the dividend behind the 2 and repeat the process: 26 / 9

Moving on to step 4:
26 divided by 9 is 2 with a remainder of 8.
The next digit of our result is 2. 
Result so far: 562.0
If we subtract 18 from 26, we get 8.
Include the next digit (3) from the dividend after 8, then repeat: 83 / 9

Step 5:
9 goes into 83 9 times with a remainder of 2.
Record the quotient 9 as the next digit in the result. 
Result so far: 5629.0
If we take 81 away from 83, we end up with 2.
Append the next digit (1) from the dividend to 2 and continue with: 21 / 9

Advancing to step 6:
9 can be fit into 21 2 times, resulting in a remainder of 3.
Write down 2 as next digit of the result. 
Result so far: 56292.0
Subtract 18 from 21 to get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Advancing to step 7:
When dividing 30 by 9, we get 3 with a remainder of 3.
The next digit of our result is 3. 
Result so far: 56292.3
If we take 27 away from 30, we end up with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Step 8:
If we divide 30 by 9, we get 3 and a remainder of 3.
Put 3 as the next digit of the answer. 
Result so far: 56292.33
Subtracting 27 from 30 leaves us with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

In conclusion, the division gives 56292.33 with a balance of 0.003.