We're dividing 102338 by 41 
Our goal is to divide 102338 by 41.

Advancing to step 1:
The number 41 fits into 1 0 times, leaving 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.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 41

Step 2:
The number 41 fits into 10 0 times, leaving a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 10 leaves us with 10.
Include the next digit (2) from the dividend after 10, then repeat: 102 / 41

Let's proceed to step 3:
If we divide 102 by 41, we get 2 and a remainder of 20.
The number 2 becomes the next digit in our result. 
Result so far: 2.0
Subtracting 82 from 102 leaves us with 20.
Include the next digit (3) from the dividend after 20, then repeat: 203 / 41

Moving on to step 4:
41 goes into 203 4 times with a remainder of 39.
Put 4 as the next digit of the answer. 
Result so far: 24.0
Subtract 164 from 203 to get 39.
Grab the next digit (3) from the dividend, add it to 39, then carry on: 393 / 41

Let's proceed to step 5:
When dividing 393 by 41, we get 9 with a remainder of 24.
Record the quotient 9 as the next digit in the result. 
Result so far: 249.0
If we take 369 away from 393, we end up with 24.
Take the next digit (8) from the dividend and append it to 24, then repeat: 248 / 41

Let's proceed to step 6:
41 goes into 248 6 times with a remainder of 2.
Use 6 as the next digit of our solution. 
Result so far: 2496.0
If we take 246 away from 248, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 7:
20 divided by 41 is 0 with a remainder of 20.
Record the quotient 0 as the next digit in the result. 
Result so far: 2496.0
The remainder is 20 after subtracting 0 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

On to step 8:
41 can be fit into 200 4 times, resulting in a remainder of 36.
The number 4 becomes the next digit in our result. 
Result so far: 2496.04
Deduct 164 from 200 and we're left with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Going ahead to step 9:
41 goes into 360 8 times with a remainder of 32.
Write down 8 as next digit of the result. 
Result so far: 2496.048
If we take 328 away from 360, we end up with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Moving on to step 10:
41 can be fit into 320 7 times, resulting in a remainder of 33.
The number 7 becomes the next digit in our result. 
Result so far: 2496.0487
The remainder is 33 after subtracting 287 from 320.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Step 11:
When dividing 330 by 41, we get 8 with a remainder of 2.
The number 8 becomes the next digit in our result. 
Result so far: 2496.04878
Deduct 328 from 330 and we're left with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Going ahead to step 12:
20 divided by 41 is 0 with a remainder of 20.
Put 0 as the next digit of the answer. 
Result so far: 2496.04878
Subtracting 0 from 20 leaves us with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Going ahead to step 13:
When dividing 200 by 41, we get 4 with a remainder of 36.
Record the quotient 4 as the next digit in the result. 
Result so far: 2496.0487804
If we take 164 away from 200, we end up with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Moving on to step 14:
When dividing 360 by 41, we get 8 with a remainder of 32.
Use 8 as the next digit of our solution. 
Result so far: 2496.04878048
The remainder is 32 after subtracting 328 from 360.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

In conclusion, the division gives 2496.04878048 with a balance of 3.2e-08.