We look at the division of 517 by 89 
We're looking to find how many times 89 goes into 517.

On to step 1:
5 divided by 89 is 0 with 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.
Fetch the next digit (1) from the dividend, attach it to 5 and continue: 51 / 89

Going ahead to step 2:
89 can be fit into 51 0 times, resulting in a remainder of 51.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 51 and we're left with 51.
Take the next digit (7) from the dividend and append it to 51, then repeat: 517 / 89

Going ahead to step 3:
When dividing 517 by 89, we get 5 with a remainder of 72.
The next digit of our result is 5. 
Result so far: 5.0
Deduct 445 from 517 and we're left with 72.
Since there are no more digits in the dividend, we add a zero to the remainder making it 720, and continue the process.

Advancing to step 4:
89 goes into 720 8 times with a remainder of 8.
The number 8 becomes the next digit in our result. 
Result so far: 5.8
If we take 712 away from 720, we end up with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

On to step 5:
The number 89 fits into 80 0 times, leaving a remainder of 80.
The number 0 becomes the next digit in our result. 
Result so far: 5.8
If we subtract 0 from 80, we get 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 800, and continue the process.

Step 6:
89 goes into 800 8 times with a remainder of 88.
The next digit of our result is 8. 
Result so far: 5.808
Subtract 712 from 800 to get 88.
Since there are no more digits in the dividend, we add a zero to the remainder making it 880, and continue the process.

Let's proceed to step 7:
89 can be fit into 880 9 times, resulting in a remainder of 79.
Put 9 as the next digit of the answer. 
Result so far: 5.8089
Subtracting 801 from 880 leaves us with 79.
Since there are no more digits in the dividend, we add a zero to the remainder making it 790, and continue the process.

Moving on to step 8:
790 divided by 89 is 8 with a remainder of 78.
Put 8 as the next digit of the answer. 
Result so far: 5.80898
Deduct 712 from 790 and we're left with 78.
Since there are no more digits in the dividend, we add a zero to the remainder making it 780, and continue the process.

Moving on to step 9:
89 goes into 780 8 times with a remainder of 68.
Write down 8 as next digit of the result. 
Result so far: 5.808988
If we take 712 away from 780, we end up with 68.
Since there are no more digits in the dividend, we add a zero to the remainder making it 680, and continue the process.

Our division results in 5.808988 with a remaining 6.8e-06.