420109 ÷ 90 
We want to figure out the number of times 420109 can be divided by 90.

Let's proceed to step 1:
4 divided by 90 is 0 with a remainder of 4.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 4 after subtracting 0 from 4.
Include the next digit (2) from the dividend after 4, then repeat: 42 / 90

Let's proceed to step 2:
90 can be fit into 42 0 times, resulting in a remainder of 42.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 42 and we're left with 42.
Take the next digit (0) from the dividend and append it to 42, then repeat: 420 / 90

Step 3:
If we divide 420 by 90, we get 4 and a remainder of 60.
Put 4 as the next digit of the answer. 
Result so far: 4.0
Subtracting 360 from 420 leaves us with 60.
Take the next digit (1) from the dividend and append it to 60, then repeat: 601 / 90

Moving on to step 4:
601 divided by 90 is 6 with a remainder of 61.
Put 6 as the next digit of the answer. 
Result so far: 46.0
Deduct 540 from 601 and we're left with 61.
Bring next digit (0) of the dividend behind the 61 and repeat the process: 610 / 90

Moving on to step 5:
90 can be fit into 610 6 times, resulting in a remainder of 70.
The number 6 becomes the next digit in our result. 
Result so far: 466.0
Subtract 540 from 610 to get 70.
Fetch the next digit (9) from the dividend, attach it to 70 and continue: 709 / 90

Step 6:
When dividing 709 by 90, we get 7 with a remainder of 79.
Write down 7 as next digit of the result. 
Result so far: 4667.0
If we take 630 away from 709, we end up with 79.
Since there are no more digits in the dividend, we add a zero to the remainder making it 790, and continue the process.

Moving on to step 7:
When dividing 790 by 90, we get 8 with a remainder of 70.
The next digit of our result is 8. 
Result so far: 4667.8
If we subtract 720 from 790, we get 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Step 8:
700 divided by 90 is 7 with a remainder of 70.
The next digit of our result is 7. 
Result so far: 4667.87
Subtracting 630 from 700 leaves us with 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Step 9:
When dividing 700 by 90, we get 7 with a remainder of 70.
Put 7 as the next digit of the answer. 
Result so far: 4667.877
Subtract 630 from 700 to get 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

The final result is 4667.877 with a remainder of 0.007.