We look at the division of 102919 by 15 
We're looking to find how many times 15 goes into 102919.

Advancing to step 1:
When dividing 1 by 15, we get 0 with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Fetch the next digit (0) from the dividend, attach it to 1 and continue: 10 / 15

Step 2:
The number 15 fits into 10 0 times, leaving a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 10 and we're left with 10.
Grab the next digit (2) from the dividend, add it to 10, then carry on: 102 / 15

Step 3:
If we divide 102 by 15, we get 6 and a remainder of 12.
Record the quotient 6 as the next digit in the result. 
Result so far: 6.0
If we take 90 away from 102, we end up with 12.
Grab the next digit (9) from the dividend, add it to 12, then carry on: 129 / 15

On to step 4:
15 can be fit into 129 8 times, resulting in a remainder of 9.
Put 8 as the next digit of the answer. 
Result so far: 68.0
The remainder is 9 after subtracting 120 from 129.
Grab the next digit (1) from the dividend, add it to 9, then carry on: 91 / 15

Step 5:
When dividing 91 by 15, we get 6 with a remainder of 1.
The number 6 becomes the next digit in our result. 
Result so far: 686.0
Subtracting 90 from 91 leaves us with 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 15

Moving on to step 6:
The number 15 fits into 19 1 times, leaving a remainder of 4.
Put 1 as the next digit of the answer. 
Result so far: 6861.0
If we take 15 away from 19, we end up with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 7:
If we divide 40 by 15, we get 2 and a remainder of 10.
Write down 2 as next digit of the result. 
Result so far: 6861.2
Subtract 30 from 40 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.

On to step 8:
15 goes into 100 6 times with a remainder of 10.
The number 6 becomes the next digit in our result. 
Result so far: 6861.26
If we take 90 away from 100, we end up 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.

Advancing to step 9:
If we divide 100 by 15, we get 6 and a remainder of 10.
The number 6 becomes the next digit in our result. 
Result so far: 6861.266
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.

The final result is 6861.266 with a remainder of 0.001.