We're dividing 586301 by 9 
Let's see how many times 9 fits into 586301.

On to step 1:
9 can be fit into 5 0 times, resulting in a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Take the next digit (8) from the dividend and append it to 5, then repeat: 58 / 9

Going ahead to step 2:
9 can be fit into 58 6 times, resulting in a remainder of 4.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
If we take 54 away from 58, we end up with 4.
Grab the next digit (6) from the dividend, add it to 4, then carry on: 46 / 9

Let's proceed to step 3:
9 goes into 46 5 times with a remainder of 1.
The next digit of our result is 5. 
Result so far: 65.0
Deduct 45 from 46 and we're left with 1.
Append the next digit (3) from the dividend to 1 and continue with: 13 / 9

Going ahead to step 4:
When dividing 13 by 9, we get 1 with a remainder of 4.
The number 1 becomes the next digit in our result. 
Result so far: 651.0
Subtracting 9 from 13 leaves us with 4.
Bring next digit (0) of the dividend behind the 4 and repeat the process: 40 / 9

Moving on to step 5:
If we divide 40 by 9, we get 4 and a remainder of 4.
The number 4 becomes the next digit in our result. 
Result so far: 6514.0
If we take 36 away from 40, we end up with 4.
Fetch the next digit (1) from the dividend, attach it to 4 and continue: 41 / 9

Step 6:
9 goes into 41 4 times with a remainder of 5.
Record the quotient 4 as the next digit in the result. 
Result so far: 65144.0
If we subtract 36 from 41, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 7:
If we divide 50 by 9, we get 5 and a remainder of 5.
The next digit of our result is 5. 
Result so far: 65144.5
Deduct 45 from 50 and we're left with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 8:
The number 9 fits into 50 5 times, leaving a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 65144.55
Deduct 45 from 50 and we're left with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

In conclusion, the division gives 65144.55 with a balance of 0.005.