We look at the division of 513987 by 9 
Our goal is to divide 513987 by 9.

Going ahead to step 1:
9 can be fit into 5 0 times, resulting in a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Include the next digit (1) from the dividend after 5, then repeat: 51 / 9

On to step 2:
9 can be fit into 51 5 times, resulting in a remainder of 6.
Use 5 as the next digit of our solution. 
Result so far: 5.0
If we subtract 45 from 51, we get 6.
Fetch the next digit (3) from the dividend, attach it to 6 and continue: 63 / 9

Step 3:
9 can be fit into 63 7 times, resulting in a remainder of 0.
Use 7 as the next digit of our solution. 
Result so far: 57.0
If we take 63 away from 63, we end up with 0.
Fetch the next digit (9) from the dividend, attach it to 0 and continue: 9 / 9

Advancing to step 4:
When dividing 9 by 9, we get 1 with a remainder of 0.
Write down 1 as next digit of the result. 
Result so far: 571.0
If we take 9 away from 9, we end up with 0.
Take the next digit (8) from the dividend and append it to 0, then repeat: 8 / 9

Moving on to step 5:
The number 9 fits into 8 0 times, leaving a remainder of 8.
Record the quotient 0 as the next digit in the result. 
Result so far: 5710.0
Deduct 0 from 8 and we're left with 8.
Grab the next digit (7) from the dividend, add it to 8, then carry on: 87 / 9

On to step 6:
9 goes into 87 9 times with a remainder of 6.
The next digit of our result is 9. 
Result so far: 57109.0
Subtract 81 from 87 to 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.

Moving on to step 7:
60 divided by 9 is 6 with a remainder of 6.
Write down 6 as next digit of the result. 
Result so far: 57109.6
Subtract 54 from 60 to 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.

Moving on to step 8:
9 can be fit into 60 6 times, resulting in a remainder of 6.
Write down 6 as next digit of the result. 
Result so far: 57109.66
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 57109.66 and a remainder of 0.006.