We're dividing 103213 by 82 
We want to divide 103213 by 82.

Advancing to step 1:
1 divided by 82 is 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.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 82

Moving on to step 2:
82 goes into 10 0 times with a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 10 to get 10.
Fetch the next digit (3) from the dividend, attach it to 10 and continue: 103 / 82

Let's proceed to step 3:
The number 82 fits into 103 1 times, leaving a remainder of 21.
The next digit of our result is 1. 
Result so far: 1.0
Deduct 82 from 103 and we're left with 21.
Take the next digit (2) from the dividend and append it to 21, then repeat: 212 / 82

Moving on to step 4:
82 can be fit into 212 2 times, resulting in a remainder of 48.
Put 2 as the next digit of the answer. 
Result so far: 12.0
Subtracting 164 from 212 leaves us with 48.
Take the next digit (1) from the dividend and append it to 48, then repeat: 481 / 82

Moving on to step 5:
The number 82 fits into 481 5 times, leaving a remainder of 71.
The number 5 becomes the next digit in our result. 
Result so far: 125.0
If we take 410 away from 481, we end up with 71.
Take the next digit (3) from the dividend and append it to 71, then repeat: 713 / 82

On to step 6:
82 can be fit into 713 8 times, resulting in a remainder of 57.
The number 8 becomes the next digit in our result. 
Result so far: 1258.0
Subtracting 656 from 713 leaves us with 57.
Since there are no more digits in the dividend, we add a zero to the remainder making it 570, and continue the process.

Let's proceed to step 7:
82 goes into 570 6 times with a remainder of 78.
Record the quotient 6 as the next digit in the result. 
Result so far: 1258.6
Subtract 492 from 570 to get 78.
Since there are no more digits in the dividend, we add a zero to the remainder making it 780, and continue the process.

Step 8:
780 divided by 82 is 9 with a remainder of 42.
The number 9 becomes the next digit in our result. 
Result so far: 1258.69
If we subtract 738 from 780, we get 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

On to step 9:
420 divided by 82 is 5 with a remainder of 10.
Use 5 as the next digit of our solution. 
Result so far: 1258.695
The remainder is 10 after subtracting 410 from 420.
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 10:
82 goes into 100 1 times with a remainder of 18.
Put 1 as the next digit of the answer. 
Result so far: 1258.6951
Subtract 82 from 100 to get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Step 11:
When dividing 180 by 82, we get 2 with a remainder of 16.
The number 2 becomes the next digit in our result. 
Result so far: 1258.69512
If we take 164 away from 180, we end up with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Step 12:
160 divided by 82 is 1 with a remainder of 78.
Use 1 as the next digit of our solution. 
Result so far: 1258.695121
Subtract 82 from 160 to get 78.
Since there are no more digits in the dividend, we add a zero to the remainder making it 780, and continue the process.

Advancing to step 13:
82 can be fit into 780 9 times, resulting in a remainder of 42.
The number 9 becomes the next digit in our result. 
Result so far: 1258.6951219
If we take 738 away from 780, 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.

Let's proceed to step 14:
When dividing 420 by 82, we get 5 with a remainder of 10.
Use 5 as the next digit of our solution. 
Result so far: 1258.69512195
If we take 410 away from 420, 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.

Our division results in 1258.69512195 with a remaining 1e-08.