596811 ÷ 9 
We're looking to find how many times 9 goes into 596811.

Step 1:
When dividing 5 by 9, we get 0 with a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Append the next digit (9) from the dividend to 5 and continue with: 59 / 9

Let's proceed to step 2:
9 can be fit into 59 6 times, resulting in a remainder of 5.
Put 6 as the next digit of the answer. 
Result so far: 6.0
If we subtract 54 from 59, we get 5.
Take the next digit (6) from the dividend and append it to 5, then repeat: 56 / 9

Advancing to step 3:
56 divided by 9 is 6 with a remainder of 2.
Put 6 as the next digit of the answer. 
Result so far: 66.0
Deduct 54 from 56 and we're left with 2.
Grab the next digit (8) from the dividend, add it to 2, then carry on: 28 / 9

Step 4:
When dividing 28 by 9, we get 3 with a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 663.0
The remainder is 1 after subtracting 27 from 28.
Append the next digit (1) from the dividend to 1 and continue with: 11 / 9

Going ahead to step 5:
9 goes into 11 1 times with a remainder of 2.
The next digit of our result is 1. 
Result so far: 6631.0
Subtracting 9 from 11 leaves us with 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 9

Moving on to step 6:
9 can be fit into 21 2 times, resulting in a remainder of 3.
The number 2 becomes the next digit in our result. 
Result so far: 66312.0
The remainder is 3 after subtracting 18 from 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

On to step 7:
When dividing 30 by 9, we get 3 with a remainder of 3.
Record the quotient 3 as the next digit in the result. 
Result so far: 66312.3
If we take 27 away from 30, we end up with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

On to step 8:
9 goes into 30 3 times with a remainder of 3.
Put 3 as the next digit of the answer. 
Result so far: 66312.33
If we subtract 27 from 30, we get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

After the division, we end up with 66312.33 and a remainder of 0.003.