We're dividing 598978 by 9 
Our goal is to divide 598978 by 9.

Advancing to step 1:
5 divided by 9 is 0 with a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Fetch the next digit (9) from the dividend, attach it to 5 and continue: 59 / 9

Step 2:
59 divided by 9 is 6 with a remainder of 5.
Use 6 as the next digit of our solution. 
Result so far: 6.0
Deduct 54 from 59 and we're left with 5.
Bring next digit (8) of the dividend behind the 5 and repeat the process: 58 / 9

Going ahead to step 3:
The number 9 fits into 58 6 times, leaving a remainder of 4.
Write down 6 as next digit of the result. 
Result so far: 66.0
If we subtract 54 from 58, we get 4.
Take the next digit (9) from the dividend and append it to 4, then repeat: 49 / 9

Moving on to step 4:
49 divided by 9 is 5 with a remainder of 4.
The number 5 becomes the next digit in our result. 
Result so far: 665.0
The remainder is 4 after subtracting 45 from 49.
Grab the next digit (7) from the dividend, add it to 4, then carry on: 47 / 9

Step 5:
9 goes into 47 5 times with a remainder of 2.
The next digit of our result is 5. 
Result so far: 6655.0
If we take 45 away from 47, we end up with 2.
Append the next digit (8) from the dividend to 2 and continue with: 28 / 9

Let's proceed to step 6:
The number 9 fits into 28 3 times, leaving a remainder of 1.
The next digit of our result is 3. 
Result so far: 66553.0
Subtracting 27 from 28 leaves us with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 7:
9 goes into 10 1 times with a remainder of 1.
The number 1 becomes the next digit in our result. 
Result so far: 66553.1
If we subtract 9 from 10, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Advancing to step 8:
10 divided by 9 is 1 with a remainder of 1.
Record the quotient 1 as the next digit in the result. 
Result so far: 66553.11
Subtracting 9 from 10 leaves us with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

In conclusion, the division gives 66553.11 with a balance of 0.001.