371415 ÷ 9 
We're looking to find how many times 9 goes into 371415.

On to step 1:
3 divided by 9 is 0 with a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Grab the next digit (7) from the dividend, add it to 3, then carry on: 37 / 9

Going ahead to step 2:
37 divided by 9 is 4 with a remainder of 1.
The next digit of our result is 4. 
Result so far: 4.0
Subtracting 36 from 37 leaves us with 1.
Append the next digit (1) from the dividend to 1 and continue with: 11 / 9

On to step 3:
9 can be fit into 11 1 times, resulting in a remainder of 2.
Put 1 as the next digit of the answer. 
Result so far: 41.0
Deduct 9 from 11 and we're left with 2.
Take the next digit (4) from the dividend and append it to 2, then repeat: 24 / 9

On to step 4:
24 divided by 9 is 2 with a remainder of 6.
Record the quotient 2 as the next digit in the result. 
Result so far: 412.0
Subtract 18 from 24 to get 6.
Append the next digit (1) from the dividend to 6 and continue with: 61 / 9

Moving on to step 5:
9 can be fit into 61 6 times, resulting in a remainder of 7.
Use 6 as the next digit of our solution. 
Result so far: 4126.0
If we take 54 away from 61, we end up with 7.
Include the next digit (5) from the dividend after 7, then repeat: 75 / 9

Going ahead to step 6:
The number 9 fits into 75 8 times, leaving a remainder of 3.
Use 8 as the next digit of our solution. 
Result so far: 41268.0
If we take 72 away from 75, 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.

Moving on to step 7:
9 can be fit into 30 3 times, resulting in a remainder of 3.
Write down 3 as next digit of the result. 
Result so far: 41268.3
Subtract 27 from 30 to get 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:
The number 9 fits into 30 3 times, leaving a remainder of 3.
Write down 3 as next digit of the result. 
Result so far: 41268.33
If we take 27 away from 30, 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.

In conclusion, the division gives 41268.33 with a balance of 0.003.