508625 ÷ 9 
We're looking to find how many times 9 goes into 508625.

Moving on to step 1:
9 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Include the next digit (0) from the dividend after 5, then repeat: 50 / 9

Step 2:
50 divided by 9 is 5 with a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 5.0
If we take 45 away from 50, we end up with 5.
Bring next digit (8) of the dividend behind the 5 and repeat the process: 58 / 9

Let's proceed to step 3:
58 divided by 9 is 6 with a remainder of 4.
Record the quotient 6 as the next digit in the result. 
Result so far: 56.0
If we take 54 away from 58, we end up with 4.
Bring next digit (6) of the dividend behind the 4 and repeat the process: 46 / 9

Advancing to step 4:
9 can be fit into 46 5 times, resulting in a remainder of 1.
The next digit of our result is 5. 
Result so far: 565.0
Subtracting 45 from 46 leaves us with 1.
Grab the next digit (2) from the dividend, add it to 1, then carry on: 12 / 9

On to step 5:
If we divide 12 by 9, we get 1 and a remainder of 3.
The number 1 becomes the next digit in our result. 
Result so far: 5651.0
If we subtract 9 from 12, we get 3.
Include the next digit (5) from the dividend after 3, then repeat: 35 / 9

On to step 6:
The number 9 fits into 35 3 times, leaving a remainder of 8.
Use 3 as the next digit of our solution. 
Result so far: 56513.0
Subtract 27 from 35 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Step 7:
The number 9 fits into 80 8 times, leaving a remainder of 8.
The number 8 becomes the next digit in our result. 
Result so far: 56513.8
The remainder is 8 after subtracting 72 from 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Going ahead to step 8:
80 divided by 9 is 8 with a remainder of 8.
Write down 8 as next digit of the result. 
Result so far: 56513.88
Subtract 72 from 80 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

The final outcome is 56513.88, with a leftover of 0.008.