We're dividing 421823 by 45 
We're looking to find how many times 45 goes into 421823.

On to step 1:
If we divide 4 by 45, we get 0 and a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 4 after subtracting 0 from 4.
Grab the next digit (2) from the dividend, add it to 4, then carry on: 42 / 45

Let's proceed to step 2:
The number 45 fits into 42 0 times, leaving a remainder of 42.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 42, we get 42.
Take the next digit (1) from the dividend and append it to 42, then repeat: 421 / 45

Let's proceed to step 3:
If we divide 421 by 45, we get 9 and a remainder of 16.
The number 9 becomes the next digit in our result. 
Result so far: 9.0
If we subtract 405 from 421, we get 16.
Grab the next digit (8) from the dividend, add it to 16, then carry on: 168 / 45

On to step 4:
The number 45 fits into 168 3 times, leaving a remainder of 33.
The number 3 becomes the next digit in our result. 
Result so far: 93.0
Subtracting 135 from 168 leaves us with 33.
Bring next digit (2) of the dividend behind the 33 and repeat the process: 332 / 45

Moving on to step 5:
45 goes into 332 7 times with a remainder of 17.
Record the quotient 7 as the next digit in the result. 
Result so far: 937.0
If we subtract 315 from 332, we get 17.
Append the next digit (3) from the dividend to 17 and continue with: 173 / 45

Advancing to step 6:
45 can be fit into 173 3 times, resulting in a remainder of 38.
The next digit of our result is 3. 
Result so far: 9373.0
Subtract 135 from 173 to get 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Going ahead to step 7:
45 goes into 380 8 times with a remainder of 20.
Write down 8 as next digit of the result. 
Result so far: 9373.8
Subtracting 360 from 380 leaves us with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Let's proceed to step 8:
The number 45 fits into 200 4 times, leaving a remainder of 20.
Use 4 as the next digit of our solution. 
Result so far: 9373.84
If we take 180 away from 200, we end up with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

On to step 9:
45 can be fit into 200 4 times, resulting in a remainder of 20.
Record the quotient 4 as the next digit in the result. 
Result so far: 9373.844
Subtract 180 from 200 to get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

In conclusion, the division gives 9373.844 with a balance of 0.002.