We're dividing 421790 by 3 
The aim is to understand the frequency of 3 in 421790.

Step 1:
The number 3 fits into 4 1 times, leaving a remainder of 1.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we take 3 away from 4, we end up with 1.
Include the next digit (2) from the dividend after 1, then repeat: 12 / 3

On to step 2:
When dividing 12 by 3, we get 4 with a remainder of 0.
Put 4 as the next digit of the answer. 
Result so far: 14.0
If we take 12 away from 12, we end up with 0.
Bring next digit (1) of the dividend behind the 0 and repeat the process: 1 / 3

Let's proceed to step 3:
3 can be fit into 1 0 times, resulting in a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 140.0
Subtract 0 from 1 to get 1.
Include the next digit (7) from the dividend after 1, then repeat: 17 / 3

On to step 4:
17 divided by 3 is 5 with a remainder of 2.
The next digit of our result is 5. 
Result so far: 1405.0
Subtracting 15 from 17 leaves us with 2.
Fetch the next digit (9) from the dividend, attach it to 2 and continue: 29 / 3

Step 5:
The number 3 fits into 29 9 times, leaving a remainder of 2.
The number 9 becomes the next digit in our result. 
Result so far: 14059.0
Deduct 27 from 29 and we're left with 2.
Bring next digit (0) of the dividend behind the 2 and repeat the process: 20 / 3

Let's proceed to step 6:
3 goes into 20 6 times with a remainder of 2.
Put 6 as the next digit of the answer. 
Result so far: 140596.0
Deduct 18 from 20 and we're left with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 7:
20 divided by 3 is 6 with a remainder of 2.
Use 6 as the next digit of our solution. 
Result so far: 140596.6
Subtracting 18 from 20 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Advancing to step 8:
3 can be fit into 20 6 times, resulting in a remainder of 2.
Use 6 as the next digit of our solution. 
Result so far: 140596.66
Subtract 18 from 20 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

The final result is 140596.66 with a remainder of 0.002.