We're dividing 415384 by 3 
Our goal is to divide 415384 by 3.

Let's proceed to step 1:
When dividing 4 by 3, we get 1 with a remainder of 1.
Write down 1 as next digit of the result. 
Result so far: 1.0
Deduct 3 from 4 and we're left with 1.
Include the next digit (1) from the dividend after 1, then repeat: 11 / 3

Step 2:
11 divided by 3 is 3 with a remainder of 2.
The number 3 becomes the next digit in our result. 
Result so far: 13.0
The remainder is 2 after subtracting 9 from 11.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 3

Let's proceed to step 3:
3 can be fit into 25 8 times, resulting in a remainder of 1.
Write down 8 as next digit of the result. 
Result so far: 138.0
If we take 24 away from 25, we end up with 1.
Take the next digit (3) from the dividend and append it to 1, then repeat: 13 / 3

Advancing to step 4:
3 can be fit into 13 4 times, resulting in a remainder of 1.
Write down 4 as next digit of the result. 
Result so far: 1384.0
If we take 12 away from 13, we end up with 1.
Append the next digit (8) from the dividend to 1 and continue with: 18 / 3

Let's proceed to step 5:
3 can be fit into 18 6 times, resulting in a remainder of 0.
Record the quotient 6 as the next digit in the result. 
Result so far: 13846.0
Subtracting 18 from 18 leaves us with 0.
Bring next digit (4) of the dividend behind the 0 and repeat the process: 4 / 3

On to step 6:
The number 3 fits into 4 1 times, leaving a remainder of 1.
The number 1 becomes the next digit in our result. 
Result so far: 138461.0
Deduct 3 from 4 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 7:
When dividing 10 by 3, we get 3 with a remainder of 1.
Use 3 as the next digit of our solution. 
Result so far: 138461.3
Subtract 9 from 10 to 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.

Advancing to step 8:
The number 3 fits into 10 3 times, leaving a remainder of 1.
The next digit of our result is 3. 
Result so far: 138461.33
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 138461.33 with a balance of 0.001.