We divide 684608 by 45
We're looking to find how many times 45 goes into 684608.

Advancing to step 1:
45 goes into 6 0 times with a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Bring next digit (8) of the dividend behind the 6 and repeat the process: 68 / 45

Step 2:
If we divide 68 by 45, we get 1 and a remainder of 23.
Write down 1 as next digit of the result. 
Result so far: 1.0
Deduct 45 from 68 and we're left with 23.
Include the next digit (4) from the dividend after 23, then repeat: 234 / 45

Moving on to step 3:
If we divide 234 by 45, we get 5 and a remainder of 9.
The next digit of our result is 5. 
Result so far: 15.0
The remainder is 9 after subtracting 225 from 234.
Include the next digit (6) from the dividend after 9, then repeat: 96 / 45

Advancing to step 4:
The number 45 fits into 96 2 times, leaving a remainder of 6.
Write down 2 as next digit of the result. 
Result so far: 152.0
If we take 90 away from 96, we end up with 6.
Fetch the next digit (0) from the dividend, attach it to 6 and continue: 60 / 45

On to step 5:
If we divide 60 by 45, we get 1 and a remainder of 15.
The next digit of our result is 1. 
Result so far: 1521.0
The remainder is 15 after subtracting 45 from 60.
Bring next digit (8) of the dividend behind the 15 and repeat the process: 158 / 45

Let's proceed to step 6:
158 divided by 45 is 3 with a remainder of 23.
The next digit of our result is 3. 
Result so far: 15213.0
If we subtract 135 from 158, we get 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Step 7:
If we divide 230 by 45, we get 5 and a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 15213.5
Subtract 225 from 230 to 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.

Step 8:
45 can be fit into 50 1 times, resulting in a remainder of 5.
The next digit of our result is 1. 
Result so far: 15213.51
The remainder is 5 after subtracting 45 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

On to step 9:
When dividing 50 by 45, we get 1 with a remainder of 5.
The next digit of our result is 1. 
Result so far: 15213.511
If we subtract 45 from 50, 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.

In conclusion, the division gives 15213.511 with a balance of 0.0005.