We look at the division of 420578 by 90 
We want to divide 420578 by 90.

Step 1:
The number 90 fits into 4 0 times, leaving a remainder of 4.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 4 after subtracting 0 from 4.
Fetch the next digit (2) from the dividend, attach it to 4 and continue: 42 / 90

Let's proceed to step 2:
The number 90 fits into 42 0 times, leaving a remainder of 42.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 42 and we're left with 42.
Include the next digit (0) from the dividend after 42, then repeat: 420 / 90

Moving on to step 3:
90 goes into 420 4 times with a remainder of 60.
Put 4 as the next digit of the answer. 
Result so far: 4.0
If we subtract 360 from 420, we get 60.
Include the next digit (5) from the dividend after 60, then repeat: 605 / 90

Going ahead to step 4:
90 goes into 605 6 times with a remainder of 65.
The number 6 becomes the next digit in our result. 
Result so far: 46.0
Subtracting 540 from 605 leaves us with 65.
Grab the next digit (7) from the dividend, add it to 65, then carry on: 657 / 90

Let's proceed to step 5:
When dividing 657 by 90, we get 7 with a remainder of 27.
Use 7 as the next digit of our solution. 
Result so far: 467.0
If we subtract 630 from 657, we get 27.
Bring next digit (8) of the dividend behind the 27 and repeat the process: 278 / 90

Step 6:
If we divide 278 by 90, we get 3 and a remainder of 8.
Write down 3 as next digit of the result. 
Result so far: 4673.0
Deduct 270 from 278 and we're left with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Going ahead to step 7:
80 divided by 90 is 0 with a remainder of 80.
Put 0 as the next digit of the answer. 
Result so far: 4673.0
Subtracting 0 from 80 leaves us with 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 800, and continue the process.

Let's proceed to step 8:
When dividing 800 by 90, we get 8 with a remainder of 80.
Put 8 as the next digit of the answer. 
Result so far: 4673.08
If we subtract 720 from 800, we get 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 800, and continue the process.

Advancing to step 9:
When dividing 800 by 90, we get 8 with a remainder of 80.
The next digit of our result is 8. 
Result so far: 4673.088
Subtracting 720 from 800 leaves us with 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 800, and continue the process.

The final result is 4673.088 with a remainder of 0.008.