We're dividing 516317 by 97 
We want to figure out the number of times 516317 can be divided by 97.

On to step 1:
The number 97 fits into 5 0 times, leaving a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Take the next digit (1) from the dividend and append it to 5, then repeat: 51 / 97

Going ahead to step 2:
If we divide 51 by 97, we get 0 and a remainder of 51.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 51, we get 51.
Fetch the next digit (6) from the dividend, attach it to 51 and continue: 516 / 97

Let's proceed to step 3:
The number 97 fits into 516 5 times, leaving a remainder of 31.
Write down 5 as next digit of the result. 
Result so far: 5.0
The remainder is 31 after subtracting 485 from 516.
Grab the next digit (3) from the dividend, add it to 31, then carry on: 313 / 97

Advancing to step 4:
313 divided by 97 is 3 with a remainder of 22.
Use 3 as the next digit of our solution. 
Result so far: 53.0
Subtract 291 from 313 to get 22.
Include the next digit (1) from the dividend after 22, then repeat: 221 / 97

Moving on to step 5:
If we divide 221 by 97, we get 2 and a remainder of 27.
Put 2 as the next digit of the answer. 
Result so far: 532.0
If we subtract 194 from 221, we get 27.
Fetch the next digit (7) from the dividend, attach it to 27 and continue: 277 / 97

Advancing to step 6:
97 can be fit into 277 2 times, resulting in a remainder of 83.
Use 2 as the next digit of our solution. 
Result so far: 5322.0
Subtracting 194 from 277 leaves us with 83.
Since there are no more digits in the dividend, we add a zero to the remainder making it 830, and continue the process.

On to step 7:
830 divided by 97 is 8 with a remainder of 54.
Put 8 as the next digit of the answer. 
Result so far: 5322.8
Subtract 776 from 830 to get 54.
Since there are no more digits in the dividend, we add a zero to the remainder making it 540, and continue the process.

Let's proceed to step 8:
The number 97 fits into 540 5 times, leaving a remainder of 55.
Put 5 as the next digit of the answer. 
Result so far: 5322.85
Subtract 485 from 540 to get 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Moving on to step 9:
97 can be fit into 550 5 times, resulting in a remainder of 65.
The next digit of our result is 5. 
Result so far: 5322.855
The remainder is 65 after subtracting 485 from 550.
Since there are no more digits in the dividend, we add a zero to the remainder making it 650, and continue the process.

The final result is 5322.855 with a remainder of 0.0065.