We look at the division of 115303 by 17 
We want to figure out the number of times 115303 can be divided by 17.

Step 1:
17 can be fit into 1 0 times, resulting in a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Take the next digit (1) from the dividend and append it to 1, then repeat: 11 / 17

Step 2:
If we divide 11 by 17, we get 0 and a remainder of 11.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 11, we end up with 11.
Grab the next digit (5) from the dividend, add it to 11, then carry on: 115 / 17

On to step 3:
The number 17 fits into 115 6 times, leaving a remainder of 13.
Write down 6 as next digit of the result. 
Result so far: 6.0
If we take 102 away from 115, we end up with 13.
Append the next digit (3) from the dividend to 13 and continue with: 133 / 17

Step 4:
17 goes into 133 7 times with a remainder of 14.
Record the quotient 7 as the next digit in the result. 
Result so far: 67.0
The remainder is 14 after subtracting 119 from 133.
Grab the next digit (0) from the dividend, add it to 14, then carry on: 140 / 17

Let's proceed to step 5:
If we divide 140 by 17, we get 8 and a remainder of 4.
Write down 8 as next digit of the result. 
Result so far: 678.0
Subtract 136 from 140 to get 4.
Include the next digit (3) from the dividend after 4, then repeat: 43 / 17

Going ahead to step 6:
The number 17 fits into 43 2 times, leaving a remainder of 9.
The next digit of our result is 2. 
Result so far: 6782.0
Deduct 34 from 43 and we're left with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Advancing to step 7:
90 divided by 17 is 5 with a remainder of 5.
Record the quotient 5 as the next digit in the result. 
Result so far: 6782.5
The remainder is 5 after subtracting 85 from 90.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Step 8:
17 goes into 50 2 times with a remainder of 16.
The number 2 becomes the next digit in our result. 
Result so far: 6782.52
The remainder is 16 after subtracting 34 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

On to step 9:
17 can be fit into 160 9 times, resulting in a remainder of 7.
Record the quotient 9 as the next digit in the result. 
Result so far: 6782.529
Deduct 153 from 160 and we're left 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.

Advancing to step 10:
The number 17 fits into 70 4 times, leaving a remainder of 2.
Put 4 as the next digit of the answer. 
Result so far: 6782.5294
If we take 68 away from 70, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 11:
The number 17 fits into 20 1 times, leaving a remainder of 3.
The next digit of our result is 1. 
Result so far: 6782.52941
If we subtract 17 from 20, we get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

On to step 12:
If we divide 30 by 17, we get 1 and a remainder of 13.
Use 1 as the next digit of our solution. 
Result so far: 6782.529411
If we subtract 17 from 30, we get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

The final outcome is 6782.529411, with a leftover of 1.3e-06.