We look at the division of 102519 by 87 
Let's see how many times 87 fits into 102519.

Step 1:
The number 87 fits into 1 0 times, leaving a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Append the next digit (0) from the dividend to 1 and continue with: 10 / 87

Going ahead to step 2:
The number 87 fits into 10 0 times, leaving a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 10 and we're left with 10.
Bring next digit (2) of the dividend behind the 10 and repeat the process: 102 / 87

Advancing to step 3:
If we divide 102 by 87, we get 1 and a remainder of 15.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Deduct 87 from 102 and we're left with 15.
Fetch the next digit (5) from the dividend, attach it to 15 and continue: 155 / 87

Moving on to step 4:
If we divide 155 by 87, we get 1 and a remainder of 68.
The number 1 becomes the next digit in our result. 
Result so far: 11.0
If we take 87 away from 155, we end up with 68.
Include the next digit (1) from the dividend after 68, then repeat: 681 / 87

Advancing to step 5:
If we divide 681 by 87, we get 7 and a remainder of 72.
Record the quotient 7 as the next digit in the result. 
Result so far: 117.0
If we take 609 away from 681, we end up with 72.
Include the next digit (9) from the dividend after 72, then repeat: 729 / 87

On to step 6:
If we divide 729 by 87, we get 8 and a remainder of 33.
The next digit of our result is 8. 
Result so far: 1178.0
If we subtract 696 from 729, we get 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Advancing to step 7:
If we divide 330 by 87, we get 3 and a remainder of 69.
Use 3 as the next digit of our solution. 
Result so far: 1178.3
If we take 261 away from 330, we end up with 69.
Since there are no more digits in the dividend, we add a zero to the remainder making it 690, and continue the process.

Going ahead to step 8:
When dividing 690 by 87, we get 7 with a remainder of 81.
Use 7 as the next digit of our solution. 
Result so far: 1178.37
Subtract 609 from 690 to get 81.
Since there are no more digits in the dividend, we add a zero to the remainder making it 810, and continue the process.

Advancing to step 9:
87 goes into 810 9 times with a remainder of 27.
Put 9 as the next digit of the answer. 
Result so far: 1178.379
Deduct 783 from 810 and we're left with 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Step 10:
270 divided by 87 is 3 with a remainder of 9.
Record the quotient 3 as the next digit in the result. 
Result so far: 1178.3793
The remainder is 9 after subtracting 261 from 270.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Moving on to step 11:
When dividing 90 by 87, we get 1 with a remainder of 3.
Record the quotient 1 as the next digit in the result. 
Result so far: 1178.37931
Deduct 87 from 90 and we're left with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Going ahead to step 12:
87 goes into 30 0 times with a remainder of 30.
The number 0 becomes the next digit in our result. 
Result so far: 1178.37931
If we subtract 0 from 30, we get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

On to step 13:
The number 87 fits into 300 3 times, leaving a remainder of 39.
The next digit of our result is 3. 
Result so far: 1178.3793103
The remainder is 39 after subtracting 261 from 300.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

On to step 14:
87 goes into 390 4 times with a remainder of 42.
Record the quotient 4 as the next digit in the result. 
Result so far: 1178.37931034
If we take 348 away from 390, we end up with 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

After the division, we end up with 1178.37931034 and a remainder of 4.2e-08.