559631 ÷ 9 
We want to divide 559631 by 9.

Moving on to step 1:
When dividing 5 by 9, we get 0 with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Grab the next digit (5) from the dividend, add it to 5, then carry on: 55 / 9

Advancing to step 2:
9 goes into 55 6 times with a remainder of 1.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
The remainder is 1 after subtracting 54 from 55.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 9

Let's proceed to step 3:
9 goes into 19 2 times with a remainder of 1.
Put 2 as the next digit of the answer. 
Result so far: 62.0
If we take 18 away from 19, we end up with 1.
Grab the next digit (6) from the dividend, add it to 1, then carry on: 16 / 9

Let's proceed to step 4:
If we divide 16 by 9, we get 1 and a remainder of 7.
The next digit of our result is 1. 
Result so far: 621.0
Subtracting 9 from 16 leaves us with 7.
Append the next digit (3) from the dividend to 7 and continue with: 73 / 9

Step 5:
73 divided by 9 is 8 with a remainder of 1.
The number 8 becomes the next digit in our result. 
Result so far: 6218.0
If we subtract 72 from 73, we get 1.
Append the next digit (1) from the dividend to 1 and continue with: 11 / 9

Moving on to step 6:
If we divide 11 by 9, we get 1 and a remainder of 2.
Record the quotient 1 as the next digit in the result. 
Result so far: 62181.0
Deduct 9 from 11 and we're left with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 7:
9 goes into 20 2 times with a remainder of 2.
Record the quotient 2 as the next digit in the result. 
Result so far: 62181.2
Subtract 18 from 20 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Going ahead to step 8:
When dividing 20 by 9, we get 2 with a remainder of 2.
The number 2 becomes the next digit in our result. 
Result so far: 62181.22
Subtract 18 from 20 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

The final outcome is 62181.22, with a leftover of 0.002.