We divide 559311 by 90
We're looking to find how many times 90 goes into 559311.

Moving on to step 1:
90 goes into 5 0 times with a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Grab the next digit (5) from the dividend, add it to 5, then carry on: 55 / 90

Going ahead to step 2:
90 can be fit into 55 0 times, resulting in a remainder of 55.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 55 to get 55.
Bring next digit (9) of the dividend behind the 55 and repeat the process: 559 / 90

Step 3:
If we divide 559 by 90, we get 6 and a remainder of 19.
The next digit of our result is 6. 
Result so far: 6.0
Deduct 540 from 559 and we're left with 19.
Append the next digit (3) from the dividend to 19 and continue with: 193 / 90

Let's proceed to step 4:
90 can be fit into 193 2 times, resulting in a remainder of 13.
Write down 2 as next digit of the result. 
Result so far: 62.0
Subtract 180 from 193 to get 13.
Include the next digit (1) from the dividend after 13, then repeat: 131 / 90

On to step 5:
131 divided by 90 is 1 with a remainder of 41.
Put 1 as the next digit of the answer. 
Result so far: 621.0
Subtracting 90 from 131 leaves us with 41.
Include the next digit (1) from the dividend after 41, then repeat: 411 / 90

Step 6:
411 divided by 90 is 4 with a remainder of 51.
Put 4 as the next digit of the answer. 
Result so far: 6214.0
Subtracting 360 from 411 leaves us with 51.
Since there are no more digits in the dividend, we add a zero to the remainder making it 510, and continue the process.

Let's proceed to step 7:
When dividing 510 by 90, we get 5 with a remainder of 60.
Use 5 as the next digit of our solution. 
Result so far: 6214.5
If we take 450 away from 510, we end up 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 8:
When dividing 600 by 90, we get 6 with a remainder of 60.
The next digit of our result is 6. 
Result so far: 6214.56
The remainder is 60 after subtracting 540 from 600.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Going ahead to step 9:
600 divided by 90 is 6 with a remainder of 60.
Record the quotient 6 as the next digit in the result. 
Result so far: 6214.566
Deduct 540 from 600 and we're left 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.

After the division, we end up with 6214.566 and a remainder of 0.006.