102819 ÷ 53 
Our goal is to divide 102819 by 53.

Moving on to step 1:
If we divide 1 by 53, we get 0 and a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 53

On to step 2:
If we divide 10 by 53, we get 0 and a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 10, we end up with 10.
Fetch the next digit (2) from the dividend, attach it to 10 and continue: 102 / 53

Moving on to step 3:
53 can be fit into 102 1 times, resulting in a remainder of 49.
The next digit of our result is 1. 
Result so far: 1.0
Subtracting 53 from 102 leaves us with 49.
Fetch the next digit (8) from the dividend, attach it to 49 and continue: 498 / 53

Advancing to step 4:
53 can be fit into 498 9 times, resulting in a remainder of 21.
The next digit of our result is 9. 
Result so far: 19.0
Deduct 477 from 498 and we're left with 21.
Include the next digit (1) from the dividend after 21, then repeat: 211 / 53

On to step 5:
The number 53 fits into 211 3 times, leaving a remainder of 52.
Write down 3 as next digit of the result. 
Result so far: 193.0
If we subtract 159 from 211, we get 52.
Take the next digit (9) from the dividend and append it to 52, then repeat: 529 / 53

Step 6:
529 divided by 53 is 9 with a remainder of 52.
Use 9 as the next digit of our solution. 
Result so far: 1939.0
If we subtract 477 from 529, we get 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

Advancing to step 7:
When dividing 520 by 53, we get 9 with a remainder of 43.
The number 9 becomes the next digit in our result. 
Result so far: 1939.9
The remainder is 43 after subtracting 477 from 520.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

Moving on to step 8:
430 divided by 53 is 8 with a remainder of 6.
The next digit of our result is 8. 
Result so far: 1939.98
Deduct 424 from 430 and we're left with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 9:
60 divided by 53 is 1 with a remainder of 7.
Put 1 as the next digit of the answer. 
Result so far: 1939.981
Subtracting 53 from 60 leaves us 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.

Going ahead to step 10:
53 can be fit into 70 1 times, resulting in a remainder of 17.
Record the quotient 1 as the next digit in the result. 
Result so far: 1939.9811
If we subtract 53 from 70, we get 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

After the division, we end up with 1939.9811 and a remainder of 0.00017.