We're dividing 421259 by 3 
The aim is to understand the frequency of 3 in 421259.

Let's proceed to step 1:
When dividing 4 by 3, we get 1 with a remainder of 1.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Deduct 3 from 4 and we're left with 1.
Fetch the next digit (2) from the dividend, attach it to 1 and continue: 12 / 3

Advancing to step 2:
If we divide 12 by 3, we get 4 and a remainder of 0.
Use 4 as the next digit of our solution. 
Result so far: 14.0
Deduct 12 from 12 and we're left with 0.
Grab the next digit (1) from the dividend, add it to 0, then carry on: 1 / 3

Moving on to step 3:
The number 3 fits into 1 0 times, leaving a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 140.0
Subtract 0 from 1 to get 1.
Fetch the next digit (2) from the dividend, attach it to 1 and continue: 12 / 3

Moving on to step 4:
3 goes into 12 4 times with a remainder of 0.
Put 4 as the next digit of the answer. 
Result so far: 1404.0
Subtracting 12 from 12 leaves us with 0.
Fetch the next digit (5) from the dividend, attach it to 0 and continue: 5 / 3

Going ahead to step 5:
If we divide 5 by 3, we get 1 and a remainder of 2.
Put 1 as the next digit of the answer. 
Result so far: 14041.0
The remainder is 2 after subtracting 3 from 5.
Bring next digit (9) of the dividend behind the 2 and repeat the process: 29 / 3

Advancing to step 6:
3 goes into 29 9 times with a remainder of 2.
Record the quotient 9 as the next digit in the result. 
Result so far: 140419.0
Subtract 27 from 29 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.

Going ahead to step 7:
3 can be fit into 20 6 times, resulting in a remainder of 2.
Put 6 as the next digit of the answer. 
Result so far: 140419.6
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.

Step 8:
The number 3 fits into 20 6 times, leaving a remainder of 2.
The next digit of our result is 6. 
Result so far: 140419.66
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.

After the division, we end up with 140419.66 and a remainder of 0.002.