We look at the division of 509194 by 42 
We're looking to find how many times 42 goes into 509194.

Moving on to step 1:
If we divide 5 by 42, we get 0 and a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Include the next digit (0) from the dividend after 5, then repeat: 50 / 42

Moving on to step 2:
If we divide 50 by 42, we get 1 and a remainder of 8.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we subtract 42 from 50, we get 8.
Bring next digit (9) of the dividend behind the 8 and repeat the process: 89 / 42

Going ahead to step 3:
If we divide 89 by 42, we get 2 and a remainder of 5.
Record the quotient 2 as the next digit in the result. 
Result so far: 12.0
The remainder is 5 after subtracting 84 from 89.
Append the next digit (1) from the dividend to 5 and continue with: 51 / 42

Let's proceed to step 4:
The number 42 fits into 51 1 times, leaving a remainder of 9.
The next digit of our result is 1. 
Result so far: 121.0
If we subtract 42 from 51, we get 9.
Grab the next digit (9) from the dividend, add it to 9, then carry on: 99 / 42

Step 5:
99 divided by 42 is 2 with a remainder of 15.
The number 2 becomes the next digit in our result. 
Result so far: 1212.0
The remainder is 15 after subtracting 84 from 99.
Take the next digit (4) from the dividend and append it to 15, then repeat: 154 / 42

Step 6:
154 divided by 42 is 3 with a remainder of 28.
Use 3 as the next digit of our solution. 
Result so far: 12123.0
If we subtract 126 from 154, we get 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Going ahead to step 7:
If we divide 280 by 42, we get 6 and a remainder of 28.
Put 6 as the next digit of the answer. 
Result so far: 12123.6
Deduct 252 from 280 and we're left with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Let's proceed to step 8:
42 goes into 280 6 times with a remainder of 28.
Use 6 as the next digit of our solution. 
Result so far: 12123.66
Deduct 252 from 280 and we're left with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

In conclusion, the division gives 12123.66 with a balance of 0.028.