We look at the division of 259518 by 41 
Our goal is to divide 259518 by 41.

On to step 1:
41 can be fit into 2 0 times, resulting in a remainder of 2.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 2 to get 2.
Fetch the next digit (5) from the dividend, attach it to 2 and continue: 25 / 41

Moving on to step 2:
41 can be fit into 25 0 times, resulting in a remainder of 25.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 25, we get 25.
Append the next digit (9) from the dividend to 25 and continue with: 259 / 41

Moving on to step 3:
259 divided by 41 is 6 with a remainder of 13.
Use 6 as the next digit of our solution. 
Result so far: 6.0
Deduct 246 from 259 and we're left with 13.
Include the next digit (5) from the dividend after 13, then repeat: 135 / 41

On to step 4:
If we divide 135 by 41, we get 3 and a remainder of 12.
Use 3 as the next digit of our solution. 
Result so far: 63.0
If we take 123 away from 135, we end up with 12.
Bring next digit (1) of the dividend behind the 12 and repeat the process: 121 / 41

On to step 5:
When dividing 121 by 41, we get 2 with a remainder of 39.
Record the quotient 2 as the next digit in the result. 
Result so far: 632.0
If we subtract 82 from 121, we get 39.
Include the next digit (8) from the dividend after 39, then repeat: 398 / 41

Moving on to step 6:
If we divide 398 by 41, we get 9 and a remainder of 29.
The number 9 becomes the next digit in our result. 
Result so far: 6329.0
If we subtract 369 from 398, we get 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Going ahead to step 7:
The number 41 fits into 290 7 times, leaving a remainder of 3.
Write down 7 as next digit of the result. 
Result so far: 6329.7
If we take 287 away from 290, we end up 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.

Let's proceed to step 8:
If we divide 30 by 41, we get 0 and a remainder of 30.
The number 0 becomes the next digit in our result. 
Result so far: 6329.7
The remainder is 30 after subtracting 0 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Going ahead to step 9:
When dividing 300 by 41, we get 7 with a remainder of 13.
Write down 7 as next digit of the result. 
Result so far: 6329.707
Subtract 287 from 300 to get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Let's proceed to step 10:
When dividing 130 by 41, we get 3 with a remainder of 7.
Record the quotient 3 as the next digit in the result. 
Result so far: 6329.7073
If we take 123 away from 130, we end up 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.

Moving on to step 11:
The number 41 fits into 70 1 times, leaving a remainder of 29.
Put 1 as the next digit of the answer. 
Result so far: 6329.70731
Subtracting 41 from 70 leaves us with 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Step 12:
41 can be fit into 290 7 times, resulting in a remainder of 3.
Put 7 as the next digit of the answer. 
Result so far: 6329.707317
Deduct 287 from 290 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.

Moving on to step 13:
30 divided by 41 is 0 with a remainder of 30.
Write down 0 as next digit of the result. 
Result so far: 6329.707317
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.

Let's proceed to step 14:
300 divided by 41 is 7 with a remainder of 13.
Use 7 as the next digit of our solution. 
Result so far: 6329.70731707
Subtracting 287 from 300 leaves us with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

In conclusion, the division gives 6329.70731707 with a balance of 1.3e-08.