Let's divide 41671 by 9
We're looking to find how many times 9 goes into 41671.

Going ahead to step 1:
When dividing 4 by 9, we get 0 with a remainder of 4.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 4, we end up with 4.
Include the next digit (1) from the dividend after 4, then repeat: 41 / 9

Let's proceed to step 2:
The number 9 fits into 41 4 times, leaving a remainder of 5.
The next digit of our result is 4. 
Result so far: 4.0
If we subtract 36 from 41, we get 5.
Take the next digit (6) from the dividend and append it to 5, then repeat: 56 / 9

Moving on to step 3:
9 goes into 56 6 times with a remainder of 2.
Record the quotient 6 as the next digit in the result. 
Result so far: 46.0
Deduct 54 from 56 and we're left with 2.
Take the next digit (7) from the dividend and append it to 2, then repeat: 27 / 9

Going ahead to step 4:
9 goes into 27 3 times with a remainder of 0.
Use 3 as the next digit of our solution. 
Result so far: 463.0
Subtract 27 from 27 to get 0.
Append the next digit (1) from the dividend to 0 and continue with: 1 / 9

Going ahead to step 5:
When dividing 1 by 9, we get 0 with a remainder of 1.
The next digit of our result is 0. 
Result so far: 4630.0
Deduct 0 from 1 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Going ahead to step 6:
The number 9 fits into 10 1 times, leaving a remainder of 1.
Use 1 as the next digit of our solution. 
Result so far: 4630.1
If we subtract 9 from 10, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 7:
9 goes into 10 1 times with a remainder of 1.
Use 1 as the next digit of our solution. 
Result so far: 4630.11
If we take 9 away from 10, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

In conclusion, the division gives 4630.11 with a balance of 0.001.