706842 ÷ 41 
Our goal is to divide 706842 by 41.

Moving on to step 1:
7 divided by 41 is 0 with a remainder of 7.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 7 leaves us with 7.
Append the next digit (0) from the dividend to 7 and continue with: 70 / 41

Going ahead to step 2:
The number 41 fits into 70 1 times, leaving a remainder of 29.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we subtract 41 from 70, we get 29.
Include the next digit (6) from the dividend after 29, then repeat: 296 / 41

Moving on to step 3:
41 can be fit into 296 7 times, resulting in a remainder of 9.
Record the quotient 7 as the next digit in the result. 
Result so far: 17.0
Deduct 287 from 296 and we're left with 9.
Take the next digit (8) from the dividend and append it to 9, then repeat: 98 / 41

Going ahead to step 4:
98 divided by 41 is 2 with a remainder of 16.
Use 2 as the next digit of our solution. 
Result so far: 172.0
If we subtract 82 from 98, we get 16.
Take the next digit (4) from the dividend and append it to 16, then repeat: 164 / 41

Advancing to step 5:
41 can be fit into 164 4 times, resulting in a remainder of 0.
The next digit of our result is 4. 
Result so far: 1724.0
The remainder is 0 after subtracting 164 from 164.
Take the next digit (2) from the dividend and append it to 0, then repeat: 2 / 41

Step 6:
41 goes into 2 0 times with a remainder of 2.
The number 0 becomes the next digit in our result. 
Result so far: 17240.0
Subtract 0 from 2 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Advancing to step 7:
The number 41 fits into 20 0 times, leaving a remainder of 20.
Use 0 as the next digit of our solution. 
Result so far: 17240.0
Deduct 0 from 20 and we're left 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 8:
If we divide 200 by 41, we get 4 and a remainder of 36.
The number 4 becomes the next digit in our result. 
Result so far: 17240.04
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.

On to step 9:
The number 41 fits into 360 8 times, leaving a remainder of 32.
The next digit of our result is 8. 
Result so far: 17240.048
Subtracting 328 from 360 leaves us 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.

On to step 10:
The number 41 fits into 320 7 times, leaving a remainder of 33.
Write down 7 as next digit of the result. 
Result so far: 17240.0487
Subtracting 287 from 320 leaves us with 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Moving on to step 11:
41 goes into 330 8 times with a remainder of 2.
Write down 8 as next digit of the result. 
Result so far: 17240.04878
Subtract 328 from 330 to get 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:
41 can be fit into 20 0 times, resulting in a remainder of 20.
Use 0 as the next digit of our solution. 
Result so far: 17240.04878
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.

Step 13:
200 divided by 41 is 4 with a remainder of 36.
The next digit of our result is 4. 
Result so far: 17240.0487804
If we subtract 164 from 200, we get 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Let's proceed to step 14:
41 can be fit into 360 8 times, resulting in a remainder of 32.
The next digit of our result is 8. 
Result so far: 17240.04878048
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.

In conclusion, the division gives 17240.04878048 with a balance of 3.2e-08.