We look at the division of 97608509 by 516 
Let's see how many times 516 fits into 97608509.

Going ahead to step 1:
When dividing 9 by 516, we get 0 with a remainder of 9.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 9 leaves us with 9.
Include the next digit (7) from the dividend after 9, then repeat: 97 / 516

Step 2:
If we divide 97 by 516, we get 0 and a remainder of 97.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 97, we end up with 97.
Bring next digit (6) of the dividend behind the 97 and repeat the process: 976 / 516

Advancing to step 3:
516 can be fit into 976 1 times, resulting in a remainder of 460.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Deduct 516 from 976 and we're left with 460.
Append the next digit (0) from the dividend to 460 and continue with: 4600 / 516

Going ahead to step 4:
When dividing 4600 by 516, we get 8 with a remainder of 472.
Use 8 as the next digit of our solution. 
Result so far: 18.0
If we subtract 4128 from 4600, we get 472.
Grab the next digit (8) from the dividend, add it to 472, then carry on: 4728 / 516

Let's proceed to step 5:
When dividing 4728 by 516, we get 9 with a remainder of 84.
Put 9 as the next digit of the answer. 
Result so far: 189.0
The remainder is 84 after subtracting 4644 from 4728.
Bring next digit (5) of the dividend behind the 84 and repeat the process: 845 / 516

Moving on to step 6:
When dividing 845 by 516, we get 1 with a remainder of 329.
Put 1 as the next digit of the answer. 
Result so far: 1891.0
The remainder is 329 after subtracting 516 from 845.
Bring next digit (0) of the dividend behind the 329 and repeat the process: 3290 / 516

Let's proceed to step 7:
516 goes into 3290 6 times with a remainder of 194.
Put 6 as the next digit of the answer. 
Result so far: 18916.0
The remainder is 194 after subtracting 3096 from 3290.
Grab the next digit (9) from the dividend, add it to 194, then carry on: 1949 / 516

Advancing to step 8:
516 goes into 1949 3 times with a remainder of 401.
Record the quotient 3 as the next digit in the result. 
Result so far: 189163.0
Subtracting 1548 from 1949 leaves us with 401.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4010, and continue the process.

On to step 9:
The number 516 fits into 4010 7 times, leaving a remainder of 398.
Put 7 as the next digit of the answer. 
Result so far: 189163.7
Deduct 3612 from 4010 and we're left with 398.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3980, and continue the process.

On to step 10:
516 can be fit into 3980 7 times, resulting in a remainder of 368.
The next digit of our result is 7. 
Result so far: 189163.77
Subtracting 3612 from 3980 leaves us with 368.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3680, and continue the process.

In conclusion, the division gives 189163.77 with a balance of 0.368.