We look at the division of 559696 by 684 
We're looking to find how many times 684 goes into 559696.

Step 1:
If we divide 5 by 684, we get 0 and a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Bring next digit (5) of the dividend behind the 5 and repeat the process: 55 / 684

Let's proceed to step 2:
684 goes into 55 0 times with a remainder of 55.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 55, we end up with 55.
Take the next digit (9) from the dividend and append it to 55, then repeat: 559 / 684

Moving on to step 3:
559 divided by 684 is 0 with a remainder of 559.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 559, we end up with 559.
Fetch the next digit (6) from the dividend, attach it to 559 and continue: 5596 / 684

On to step 4:
The number 684 fits into 5596 8 times, leaving a remainder of 124.
Record the quotient 8 as the next digit in the result. 
Result so far: 8.0
Subtract 5472 from 5596 to get 124.
Take the next digit (9) from the dividend and append it to 124, then repeat: 1249 / 684

Let's proceed to step 5:
The number 684 fits into 1249 1 times, leaving a remainder of 565.
Put 1 as the next digit of the answer. 
Result so far: 81.0
If we take 684 away from 1249, we end up with 565.
Bring next digit (6) of the dividend behind the 565 and repeat the process: 5656 / 684

Step 6:
The number 684 fits into 5656 8 times, leaving a remainder of 184.
The next digit of our result is 8. 
Result so far: 818.0
Subtracting 5472 from 5656 leaves us with 184.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1840, and continue the process.

Step 7:
1840 divided by 684 is 2 with a remainder of 472.
The next digit of our result is 2. 
Result so far: 818.2
Deduct 1368 from 1840 and we're left with 472.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4720, and continue the process.

Let's proceed to step 8:
684 can be fit into 4720 6 times, resulting in a remainder of 616.
Use 6 as the next digit of our solution. 
Result so far: 818.26
If we subtract 4104 from 4720, we get 616.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6160, and continue the process.

On to step 9:
6160 divided by 684 is 9 with a remainder of 4.
Put 9 as the next digit of the answer. 
Result so far: 818.269
Subtract 6156 from 6160 to 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.

Advancing to step 10:
If we divide 40 by 684, we get 0 and a remainder of 40.
Put 0 as the next digit of the answer. 
Result so far: 818.269
If we subtract 0 from 40, we get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Advancing to step 11:
When dividing 400 by 684, we get 0 with a remainder of 400.
Write down 0 as next digit of the result. 
Result so far: 818.269
Subtract 0 from 400 to get 400.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4000, and continue the process.

After the division, we end up with 818.269 and a remainder of 0.0004.