We're dividing 558082 by 45 
Let's see how many times 45 fits into 558082.

On to step 1:
When dividing 5 by 45, we get 0 with a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Fetch the next digit (5) from the dividend, attach it to 5 and continue: 55 / 45

Going ahead to step 2:
If we divide 55 by 45, we get 1 and a remainder of 10.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we subtract 45 from 55, we get 10.
Include the next digit (8) from the dividend after 10, then repeat: 108 / 45

Advancing to step 3:
If we divide 108 by 45, we get 2 and a remainder of 18.
Record the quotient 2 as the next digit in the result. 
Result so far: 12.0
Subtract 90 from 108 to get 18.
Append the next digit (0) from the dividend to 18 and continue with: 180 / 45

On to step 4:
The number 45 fits into 180 4 times, leaving a remainder of 0.
The next digit of our result is 4. 
Result so far: 124.0
The remainder is 0 after subtracting 180 from 180.
Fetch the next digit (8) from the dividend, attach it to 0 and continue: 8 / 45

Let's proceed to step 5:
8 divided by 45 is 0 with a remainder of 8.
Write down 0 as next digit of the result. 
Result so far: 1240.0
Subtract 0 from 8 to get 8.
Bring next digit (2) of the dividend behind the 8 and repeat the process: 82 / 45

Advancing to step 6:
82 divided by 45 is 1 with a remainder of 37.
Use 1 as the next digit of our solution. 
Result so far: 12401.0
If we take 45 away from 82, we end up with 37.
Since there are no more digits in the dividend, we add a zero to the remainder making it 370, and continue the process.

Advancing to step 7:
When dividing 370 by 45, we get 8 with a remainder of 10.
Put 8 as the next digit of the answer. 
Result so far: 12401.8
If we take 360 away from 370, we end up with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 8:
If we divide 100 by 45, we get 2 and a remainder of 10.
The next digit of our result is 2. 
Result so far: 12401.82
If we take 90 away from 100, we end up with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 9:
100 divided by 45 is 2 with a remainder of 10.
Use 2 as the next digit of our solution. 
Result so far: 12401.822
If we subtract 90 from 100, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

After the division, we end up with 12401.822 and a remainder of 0.001.