135412 ÷ 42 
Our goal is to divide 135412 by 42.

Let's proceed to step 1:
When dividing 1 by 42, we get 0 with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Take the next digit (3) from the dividend and append it to 1, then repeat: 13 / 42

On to step 2:
When dividing 13 by 42, we get 0 with a remainder of 13.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 13 and we're left with 13.
Take the next digit (5) from the dividend and append it to 13, then repeat: 135 / 42

Let's proceed to step 3:
If we divide 135 by 42, we get 3 and a remainder of 9.
Write down 3 as next digit of the result. 
Result so far: 3.0
The remainder is 9 after subtracting 126 from 135.
Include the next digit (4) from the dividend after 9, then repeat: 94 / 42

Moving on to step 4:
If we divide 94 by 42, we get 2 and a remainder of 10.
Use 2 as the next digit of our solution. 
Result so far: 32.0
If we subtract 84 from 94, we get 10.
Append the next digit (1) from the dividend to 10 and continue with: 101 / 42

On to step 5:
When dividing 101 by 42, we get 2 with a remainder of 17.
The number 2 becomes the next digit in our result. 
Result so far: 322.0
If we subtract 84 from 101, we get 17.
Include the next digit (2) from the dividend after 17, then repeat: 172 / 42

Advancing to step 6:
The number 42 fits into 172 4 times, leaving a remainder of 4.
Put 4 as the next digit of the answer. 
Result so far: 3224.0
If we subtract 168 from 172, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Going ahead to step 7:
42 goes into 40 0 times with a remainder of 40.
The next digit of our result is 0. 
Result so far: 3224.0
Subtracting 0 from 40 leaves us with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

On to step 8:
If we divide 400 by 42, we get 9 and a remainder of 22.
The next digit of our result is 9. 
Result so far: 3224.09
The remainder is 22 after subtracting 378 from 400.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Let's proceed to step 9:
42 goes into 220 5 times with a remainder of 10.
The number 5 becomes the next digit in our result. 
Result so far: 3224.095
If we subtract 210 from 220, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 10:
If we divide 100 by 42, we get 2 and a remainder of 16.
Record the quotient 2 as the next digit in the result. 
Result so far: 3224.0952
The remainder is 16 after subtracting 84 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Step 11:
The number 42 fits into 160 3 times, leaving a remainder of 34.
The next digit of our result is 3. 
Result so far: 3224.09523
Deduct 126 from 160 and we're left with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Let's proceed to step 12:
340 divided by 42 is 8 with a remainder of 4.
Use 8 as the next digit of our solution. 
Result so far: 3224.095238
Deduct 336 from 340 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Let's proceed to step 13:
42 goes into 40 0 times with a remainder of 40.
Use 0 as the next digit of our solution. 
Result so far: 3224.095238
Subtracting 0 from 40 leaves us with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Step 14:
When dividing 400 by 42, we get 9 with a remainder of 22.
Write down 9 as next digit of the result. 
Result so far: 3224.09523809
Subtracting 378 from 400 leaves us with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Our division results in 3224.09523809 with a remaining 2.2e-08.