511585 ÷ 9 
Our goal is to divide 511585 by 9.

Advancing to step 1:
9 goes into 5 0 times with 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.
Append the next digit (1) from the dividend to 5 and continue with: 51 / 9

On to step 2:
51 divided by 9 is 5 with a remainder of 6.
Write down 5 as next digit of the result. 
Result so far: 5.0
The remainder is 6 after subtracting 45 from 51.
Append the next digit (1) from the dividend to 6 and continue with: 61 / 9

Advancing to step 3:
61 divided by 9 is 6 with a remainder of 7.
Put 6 as the next digit of the answer. 
Result so far: 56.0
If we take 54 away from 61, we end up with 7.
Fetch the next digit (5) from the dividend, attach it to 7 and continue: 75 / 9

Let's proceed to step 4:
75 divided by 9 is 8 with a remainder of 3.
Use 8 as the next digit of our solution. 
Result so far: 568.0
Subtract 72 from 75 to get 3.
Fetch the next digit (8) from the dividend, attach it to 3 and continue: 38 / 9

Advancing to step 5:
38 divided by 9 is 4 with a remainder of 2.
Write down 4 as next digit of the result. 
Result so far: 5684.0
Deduct 36 from 38 and we're left with 2.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 9

On to step 6:
When dividing 25 by 9, we get 2 with a remainder of 7.
Put 2 as the next digit of the answer. 
Result so far: 56842.0
Subtract 18 from 25 to get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Advancing to step 7:
9 goes into 70 7 times with a remainder of 7.
Record the quotient 7 as the next digit in the result. 
Result so far: 56842.7
Subtracting 63 from 70 leaves us with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Step 8:
If we divide 70 by 9, we get 7 and a remainder of 7.
The number 7 becomes the next digit in our result. 
Result so far: 56842.77
Subtracting 63 from 70 leaves us with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Our division results in 56842.77 with a remaining 0.007.