We're dividing 406 by 3 
Our goal is to divide 406 by 3.

Let's proceed to step 1:
If we divide 4 by 3, we get 1 and a remainder of 1.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
The remainder is 1 after subtracting 3 from 4.
Append the next digit (0) from the dividend to 1 and continue with: 10 / 3

Advancing to step 2:
The number 3 fits into 10 3 times, leaving a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 13.0
If we take 9 away from 10, we end up with 1.
Include the next digit (6) from the dividend after 1, then repeat: 16 / 3

On to step 3:
3 goes into 16 5 times with a remainder of 1.
The number 5 becomes the next digit in our result. 
Result so far: 135.0
Deduct 15 from 16 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 4:
10 divided by 3 is 3 with a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 135.3
Subtracting 9 from 10 leaves us 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.

Advancing to step 5:
3 can be fit into 10 3 times, resulting in a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 135.33
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.

After the division, we end up with 135.33 and a remainder of 0.001.