We're dividing 509742 by 85 
Our goal is to divide 509742 by 85.

Step 1:
5 divided by 85 is 0 with a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Grab the next digit (0) from the dividend, add it to 5, then carry on: 50 / 85

Moving on to step 2:
If we divide 50 by 85, we get 0 and a remainder of 50.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 50 to get 50.
Grab the next digit (9) from the dividend, add it to 50, then carry on: 509 / 85

Step 3:
If we divide 509 by 85, we get 5 and a remainder of 84.
Use 5 as the next digit of our solution. 
Result so far: 5.0
Subtract 425 from 509 to get 84.
Bring next digit (7) of the dividend behind the 84 and repeat the process: 847 / 85

On to step 4:
If we divide 847 by 85, we get 9 and a remainder of 82.
Write down 9 as next digit of the result. 
Result so far: 59.0
Deduct 765 from 847 and we're left with 82.
Take the next digit (4) from the dividend and append it to 82, then repeat: 824 / 85

Moving on to step 5:
824 divided by 85 is 9 with a remainder of 59.
The next digit of our result is 9. 
Result so far: 599.0
If we take 765 away from 824, we end up with 59.
Grab the next digit (2) from the dividend, add it to 59, then carry on: 592 / 85

Step 6:
When dividing 592 by 85, we get 6 with a remainder of 82.
Record the quotient 6 as the next digit in the result. 
Result so far: 5996.0
Subtracting 510 from 592 leaves us with 82.
Since there are no more digits in the dividend, we add a zero to the remainder making it 820, and continue the process.

Let's proceed to step 7:
When dividing 820 by 85, we get 9 with a remainder of 55.
Use 9 as the next digit of our solution. 
Result so far: 5996.9
Subtracting 765 from 820 leaves us with 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Let's proceed to step 8:
When dividing 550 by 85, we get 6 with a remainder of 40.
The number 6 becomes the next digit in our result. 
Result so far: 5996.96
Subtracting 510 from 550 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 9:
The number 85 fits into 400 4 times, leaving a remainder of 60.
Write down 4 as next digit of the result. 
Result so far: 5996.964
Subtracting 340 from 400 leaves us with 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Moving on to step 10:
85 can be fit into 600 7 times, resulting in a remainder of 5.
Put 7 as the next digit of the answer. 
Result so far: 5996.9647
The remainder is 5 after subtracting 595 from 600.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 11:
When dividing 50 by 85, we get 0 with a remainder of 50.
Record the quotient 0 as the next digit in the result. 
Result so far: 5996.9647
Subtract 0 from 50 to get 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Moving on to step 12:
85 can be fit into 500 5 times, resulting in a remainder of 75.
Write down 5 as next digit of the result. 
Result so far: 5996.964705
Deduct 425 from 500 and we're left with 75.
Since there are no more digits in the dividend, we add a zero to the remainder making it 750, and continue the process.

Moving on to step 13:
If we divide 750 by 85, we get 8 and a remainder of 70.
Record the quotient 8 as the next digit in the result. 
Result so far: 5996.9647058
The remainder is 70 after subtracting 680 from 750.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Moving on to step 14:
The number 85 fits into 700 8 times, leaving a remainder of 20.
Record the quotient 8 as the next digit in the result. 
Result so far: 5996.96470588
The remainder is 20 after subtracting 680 from 700.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

In conclusion, the division gives 5996.96470588 with a balance of 2e-08.