341259 ÷ 9 
We want to figure out the number of times 341259 can be divided by 9.

Advancing to step 1:
9 goes into 3 0 times with a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 3 to get 3.
Take the next digit (4) from the dividend and append it to 3, then repeat: 34 / 9

Step 2:
9 can be fit into 34 3 times, resulting in a remainder of 7.
Put 3 as the next digit of the answer. 
Result so far: 3.0
The remainder is 7 after subtracting 27 from 34.
Grab the next digit (1) from the dividend, add it to 7, then carry on: 71 / 9

On to step 3:
If we divide 71 by 9, we get 7 and a remainder of 8.
Use 7 as the next digit of our solution. 
Result so far: 37.0
The remainder is 8 after subtracting 63 from 71.
Append the next digit (2) from the dividend to 8 and continue with: 82 / 9

Let's proceed to step 4:
When dividing 82 by 9, we get 9 with a remainder of 1.
The next digit of our result is 9. 
Result so far: 379.0
If we subtract 81 from 82, we get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 9

Advancing to step 5:
The number 9 fits into 15 1 times, leaving a remainder of 6.
Record the quotient 1 as the next digit in the result. 
Result so far: 3791.0
If we subtract 9 from 15, we get 6.
Take the next digit (9) from the dividend and append it to 6, then repeat: 69 / 9

Advancing to step 6:
If we divide 69 by 9, we get 7 and a remainder of 6.
Put 7 as the next digit of the answer. 
Result so far: 37917.0
If we take 63 away from 69, we end up with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

On to step 7:
When dividing 60 by 9, we get 6 with a remainder of 6.
Record the quotient 6 as the next digit in the result. 
Result so far: 37917.6
Deduct 54 from 60 and we're left with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Let's proceed to step 8:
When dividing 60 by 9, we get 6 with a remainder of 6.
Use 6 as the next digit of our solution. 
Result so far: 37917.66
Subtract 54 from 60 to get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

The final result is 37917.66 with a remainder of 0.006.