We're dividing 257454 by 41 
Our goal is to divide 257454 by 41.

Step 1:
2 divided by 41 is 0 with a remainder of 2.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 2, we get 2.
Append the next digit (5) from the dividend to 2 and continue with: 25 / 41

Moving on to step 2:
When dividing 25 by 41, we get 0 with a remainder of 25.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 25, we end up with 25.
Include the next digit (7) from the dividend after 25, then repeat: 257 / 41

Moving on to step 3:
The number 41 fits into 257 6 times, leaving a remainder of 11.
Write down 6 as next digit of the result. 
Result so far: 6.0
Subtract 246 from 257 to get 11.
Grab the next digit (4) from the dividend, add it to 11, then carry on: 114 / 41

Going ahead to step 4:
114 divided by 41 is 2 with a remainder of 32.
Record the quotient 2 as the next digit in the result. 
Result so far: 62.0
Subtract 82 from 114 to get 32.
Append the next digit (5) from the dividend to 32 and continue with: 325 / 41

Let's proceed to step 5:
325 divided by 41 is 7 with a remainder of 38.
The number 7 becomes the next digit in our result. 
Result so far: 627.0
If we subtract 287 from 325, we get 38.
Grab the next digit (4) from the dividend, add it to 38, then carry on: 384 / 41

Going ahead to step 6:
41 can be fit into 384 9 times, resulting in a remainder of 15.
Use 9 as the next digit of our solution. 
Result so far: 6279.0
Deduct 369 from 384 and we're left with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Advancing to step 7:
41 can be fit into 150 3 times, resulting in a remainder of 27.
Put 3 as the next digit of the answer. 
Result so far: 6279.3
Deduct 123 from 150 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.

Let's proceed to step 8:
If we divide 270 by 41, we get 6 and a remainder of 24.
Write down 6 as next digit of the result. 
Result so far: 6279.36
Subtracting 246 from 270 leaves us with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Let's proceed to step 9:
41 can be fit into 240 5 times, resulting in a remainder of 35.
Write down 5 as next digit of the result. 
Result so far: 6279.365
Subtract 205 from 240 to get 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Going ahead to step 10:
350 divided by 41 is 8 with a remainder of 22.
Put 8 as the next digit of the answer. 
Result so far: 6279.3658
If we subtract 328 from 350, we get 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Advancing to step 11:
The number 41 fits into 220 5 times, leaving a remainder of 15.
The next digit of our result is 5. 
Result so far: 6279.36585
Subtract 205 from 220 to get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Let's proceed to step 12:
The number 41 fits into 150 3 times, leaving a remainder of 27.
Record the quotient 3 as the next digit in the result. 
Result so far: 6279.365853
The remainder is 27 after subtracting 123 from 150.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Going ahead to step 13:
41 can be fit into 270 6 times, resulting in a remainder of 24.
Use 6 as the next digit of our solution. 
Result so far: 6279.3658536
Deduct 246 from 270 and we're left with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Step 14:
When dividing 240 by 41, we get 5 with a remainder of 35.
The number 5 becomes the next digit in our result. 
Result so far: 6279.36585365
Subtracting 205 from 240 leaves us with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

In conclusion, the division gives 6279.36585365 with a balance of 3.5e-08.