We're dividing 677000 by 90 
We want to figure out the number of times 677000 can be divided by 90.

Going ahead to step 1:
6 divided by 90 is 0 with a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 6, we get 6.
Bring next digit (7) of the dividend behind the 6 and repeat the process: 67 / 90

Step 2:
When dividing 67 by 90, we get 0 with a remainder of 67.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 67 to get 67.
Bring next digit (7) of the dividend behind the 67 and repeat the process: 677 / 90

Going ahead to step 3:
When dividing 677 by 90, we get 7 with a remainder of 47.
Record the quotient 7 as the next digit in the result. 
Result so far: 7.0
Deduct 630 from 677 and we're left with 47.
Bring next digit (0) of the dividend behind the 47 and repeat the process: 470 / 90

Step 4:
If we divide 470 by 90, we get 5 and a remainder of 20.
The next digit of our result is 5. 
Result so far: 75.0
If we subtract 450 from 470, we get 20.
Bring next digit (0) of the dividend behind the 20 and repeat the process: 200 / 90

Going ahead to step 5:
90 can be fit into 200 2 times, resulting in a remainder of 20.
Use 2 as the next digit of our solution. 
Result so far: 752.0
If we subtract 180 from 200, we get 20.
Include the next digit (0) from the dividend after 20, then repeat: 200 / 90

Step 6:
90 goes into 200 2 times with a remainder of 20.
Write down 2 as next digit of the result. 
Result so far: 7522.0
Deduct 180 from 200 and we're left 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 7:
200 divided by 90 is 2 with a remainder of 20.
Put 2 as the next digit of the answer. 
Result so far: 7522.2
Subtracting 180 from 200 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.

Advancing to step 8:
The number 90 fits into 200 2 times, leaving a remainder of 20.
Record the quotient 2 as the next digit in the result. 
Result so far: 7522.22
The remainder is 20 after subtracting 180 from 200.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

The final result is 7522.22 with a remainder of 0.02.