505774 ÷ 45 
Our goal is to divide 505774 by 45.

Let's proceed to step 1:
45 goes into 5 0 times with a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Grab the next digit (0) from the dividend, add it to 5, then carry on: 50 / 45

Moving on to step 2:
The number 45 fits into 50 1 times, leaving a remainder of 5.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtract 45 from 50 to get 5.
Append the next digit (5) from the dividend to 5 and continue with: 55 / 45

On to step 3:
45 can be fit into 55 1 times, resulting in a remainder of 10.
The number 1 becomes the next digit in our result. 
Result so far: 11.0
The remainder is 10 after subtracting 45 from 55.
Bring next digit (7) of the dividend behind the 10 and repeat the process: 107 / 45

Going ahead to step 4:
107 divided by 45 is 2 with a remainder of 17.
The next digit of our result is 2. 
Result so far: 112.0
Subtracting 90 from 107 leaves us with 17.
Include the next digit (7) from the dividend after 17, then repeat: 177 / 45

Step 5:
45 can be fit into 177 3 times, resulting in a remainder of 42.
Put 3 as the next digit of the answer. 
Result so far: 1123.0
Subtract 135 from 177 to get 42.
Include the next digit (4) from the dividend after 42, then repeat: 424 / 45

Moving on to step 6:
If we divide 424 by 45, we get 9 and a remainder of 19.
Use 9 as the next digit of our solution. 
Result so far: 11239.0
If we take 405 away from 424, we end up with 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

On to step 7:
The number 45 fits into 190 4 times, leaving a remainder of 10.
Write down 4 as next digit of the result. 
Result so far: 11239.4
If we take 180 away from 190, 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.

Step 8:
45 can be fit into 100 2 times, resulting in a remainder of 10.
The next digit of our result is 2. 
Result so far: 11239.42
Deduct 90 from 100 and we're left 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.

Let's proceed to step 9:
45 can be fit into 100 2 times, resulting in a remainder of 10.
Put 2 as the next digit of the answer. 
Result so far: 11239.422
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.

The final result is 11239.422 with a remainder of 0.001.