645377 ÷ 90 
Our goal is to divide 645377 by 90.

Step 1:
6 divided by 90 is 0 with a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Include the next digit (4) from the dividend after 6, then repeat: 64 / 90

Let's proceed to step 2:
The number 90 fits into 64 0 times, leaving a remainder of 64.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 64, we get 64.
Take the next digit (5) from the dividend and append it to 64, then repeat: 645 / 90

On to step 3:
645 divided by 90 is 7 with a remainder of 15.
Record the quotient 7 as the next digit in the result. 
Result so far: 7.0
Subtracting 630 from 645 leaves us with 15.
Append the next digit (3) from the dividend to 15 and continue with: 153 / 90

Let's proceed to step 4:
90 can be fit into 153 1 times, resulting in a remainder of 63.
The next digit of our result is 1. 
Result so far: 71.0
If we subtract 90 from 153, we get 63.
Include the next digit (7) from the dividend after 63, then repeat: 637 / 90

Moving on to step 5:
90 can be fit into 637 7 times, resulting in a remainder of 7.
Record the quotient 7 as the next digit in the result. 
Result so far: 717.0
Subtracting 630 from 637 leaves us with 7.
Fetch the next digit (7) from the dividend, attach it to 7 and continue: 77 / 90

Let's proceed to step 6:
If we divide 77 by 90, we get 0 and a remainder of 77.
Use 0 as the next digit of our solution. 
Result so far: 7170.0
Deduct 0 from 77 and we're left with 77.
Since there are no more digits in the dividend, we add a zero to the remainder making it 770, and continue the process.

On to step 7:
90 goes into 770 8 times with a remainder of 50.
The number 8 becomes the next digit in our result. 
Result so far: 7170.8
The remainder is 50 after subtracting 720 from 770.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Advancing to step 8:
The number 90 fits into 500 5 times, leaving a remainder of 50.
Use 5 as the next digit of our solution. 
Result so far: 7170.85
If we take 450 away from 500, we end up with 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Moving on to step 9:
500 divided by 90 is 5 with a remainder of 50.
Use 5 as the next digit of our solution. 
Result so far: 7170.855
Subtract 450 from 500 to get 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

The final outcome is 7170.855, with a leftover of 0.005.