We divide 103303 by 15
Our goal is to divide 103303 by 15.

Going ahead to step 1:
1 divided by 15 is 0 with a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 15

Moving on to step 2:
The number 15 fits into 10 0 times, leaving a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 10 and we're left with 10.
Include the next digit (3) from the dividend after 10, then repeat: 103 / 15

On to step 3:
The number 15 fits into 103 6 times, leaving a remainder of 13.
Put 6 as the next digit of the answer. 
Result so far: 6.0
If we take 90 away from 103, we end up with 13.
Grab the next digit (3) from the dividend, add it to 13, then carry on: 133 / 15

Advancing to step 4:
133 divided by 15 is 8 with a remainder of 13.
The next digit of our result is 8. 
Result so far: 68.0
The remainder is 13 after subtracting 120 from 133.
Fetch the next digit (0) from the dividend, attach it to 13 and continue: 130 / 15

Step 5:
When dividing 130 by 15, we get 8 with a remainder of 10.
Use 8 as the next digit of our solution. 
Result so far: 688.0
Subtracting 120 from 130 leaves us with 10.
Include the next digit (3) from the dividend after 10, then repeat: 103 / 15

Going ahead to step 6:
If we divide 103 by 15, we get 6 and a remainder of 13.
Use 6 as the next digit of our solution. 
Result so far: 6886.0
The remainder is 13 after subtracting 90 from 103.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Step 7:
The number 15 fits into 130 8 times, leaving a remainder of 10.
Put 8 as the next digit of the answer. 
Result so far: 6886.8
Deduct 120 from 130 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 8:
When dividing 100 by 15, we get 6 with a remainder of 10.
Use 6 as the next digit of our solution. 
Result so far: 6886.86
Subtract 90 from 100 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 9:
The number 15 fits into 100 6 times, leaving a remainder of 10.
Use 6 as the next digit of our solution. 
Result so far: 6886.866
If we subtract 90 from 100, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

After the division, we end up with 6886.866 and a remainder of 0.001.