509446 ÷ 84 
We want to figure out the number of times 509446 can be divided by 84.

Advancing to step 1:
84 goes into 5 0 times with a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Take the next digit (0) from the dividend and append it to 5, then repeat: 50 / 84

Going ahead to step 2:
50 divided by 84 is 0 with a remainder of 50.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 50, we get 50.
Bring next digit (9) of the dividend behind the 50 and repeat the process: 509 / 84

Step 3:
If we divide 509 by 84, we get 6 and a remainder of 5.
Write down 6 as next digit of the result. 
Result so far: 6.0
If we take 504 away from 509, we end up with 5.
Append the next digit (4) from the dividend to 5 and continue with: 54 / 84

Moving on to step 4:
If we divide 54 by 84, we get 0 and a remainder of 54.
The next digit of our result is 0. 
Result so far: 60.0
If we take 0 away from 54, we end up with 54.
Bring next digit (4) of the dividend behind the 54 and repeat the process: 544 / 84

Advancing to step 5:
84 can be fit into 544 6 times, resulting in a remainder of 40.
Record the quotient 6 as the next digit in the result. 
Result so far: 606.0
The remainder is 40 after subtracting 504 from 544.
Bring next digit (6) of the dividend behind the 40 and repeat the process: 406 / 84

Advancing to step 6:
84 can be fit into 406 4 times, resulting in a remainder of 70.
The next digit of our result is 4. 
Result so far: 6064.0
Subtract 336 from 406 to get 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Advancing to step 7:
When dividing 700 by 84, we get 8 with a remainder of 28.
The number 8 becomes the next digit in our result. 
Result so far: 6064.8
The remainder is 28 after subtracting 672 from 700.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Step 8:
84 can be fit into 280 3 times, resulting in a remainder of 28.
The next digit of our result is 3. 
Result so far: 6064.83
Subtracting 252 from 280 leaves us 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.

On to step 9:
280 divided by 84 is 3 with a remainder of 28.
Put 3 as the next digit of the answer. 
Result so far: 6064.833
The remainder is 28 after subtracting 252 from 280.
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 6064.833 with a balance of 0.0028.