We're dividing 542303 by 45 
We're looking to find how many times 45 goes into 542303.

Going ahead to step 1:
The number 45 fits into 5 0 times, leaving a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Fetch the next digit (4) from the dividend, attach it to 5 and continue: 54 / 45

Let's proceed to step 2:
54 divided by 45 is 1 with a remainder of 9.
Put 1 as the next digit of the answer. 
Result so far: 1.0
If we take 45 away from 54, we end up with 9.
Append the next digit (2) from the dividend to 9 and continue with: 92 / 45

On to step 3:
92 divided by 45 is 2 with a remainder of 2.
Use 2 as the next digit of our solution. 
Result so far: 12.0
The remainder is 2 after subtracting 90 from 92.
Append the next digit (3) from the dividend to 2 and continue with: 23 / 45

Advancing to step 4:
When dividing 23 by 45, we get 0 with a remainder of 23.
The next digit of our result is 0. 
Result so far: 120.0
Deduct 0 from 23 and we're left with 23.
Fetch the next digit (0) from the dividend, attach it to 23 and continue: 230 / 45

Step 5:
45 goes into 230 5 times with a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 1205.0
Subtract 225 from 230 to get 5.
Fetch the next digit (3) from the dividend, attach it to 5 and continue: 53 / 45

Let's proceed to step 6:
53 divided by 45 is 1 with a remainder of 8.
The number 1 becomes the next digit in our result. 
Result so far: 12051.0
If we subtract 45 from 53, we get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

On to step 7:
45 goes into 80 1 times with a remainder of 35.
Put 1 as the next digit of the answer. 
Result so far: 12051.1
Subtracting 45 from 80 leaves us with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Moving on to step 8:
45 goes into 350 7 times with a remainder of 35.
Use 7 as the next digit of our solution. 
Result so far: 12051.17
Subtracting 315 from 350 leaves us with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Moving on to step 9:
When dividing 350 by 45, we get 7 with a remainder of 35.
The number 7 becomes the next digit in our result. 
Result so far: 12051.177
If we subtract 315 from 350, we get 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

After the division, we end up with 12051.177 and a remainder of 0.0035.