We're dividing 777557 by 9 
The aim is to understand the frequency of 9 in 777557.

Going ahead to step 1:
The number 9 fits into 7 0 times, leaving a remainder of 7.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 7 and we're left with 7.
Fetch the next digit (7) from the dividend, attach it to 7 and continue: 77 / 9

Going ahead to step 2:
The number 9 fits into 77 8 times, leaving a remainder of 5.
Record the quotient 8 as the next digit in the result. 
Result so far: 8.0
Deduct 72 from 77 and we're left with 5.
Fetch the next digit (7) from the dividend, attach it to 5 and continue: 57 / 9

Going ahead to step 3:
If we divide 57 by 9, we get 6 and a remainder of 3.
Record the quotient 6 as the next digit in the result. 
Result so far: 86.0
Subtract 54 from 57 to get 3.
Bring next digit (5) of the dividend behind the 3 and repeat the process: 35 / 9

On to step 4:
The number 9 fits into 35 3 times, leaving a remainder of 8.
Record the quotient 3 as the next digit in the result. 
Result so far: 863.0
Subtracting 27 from 35 leaves us with 8.
Include the next digit (5) from the dividend after 8, then repeat: 85 / 9

Moving on to step 5:
85 divided by 9 is 9 with a remainder of 4.
The number 9 becomes the next digit in our result. 
Result so far: 8639.0
Subtracting 81 from 85 leaves us with 4.
Append the next digit (7) from the dividend to 4 and continue with: 47 / 9

Moving on to step 6:
9 goes into 47 5 times with a remainder of 2.
The next digit of our result is 5. 
Result so far: 86395.0
If we subtract 45 from 47, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 7:
9 can be fit into 20 2 times, resulting in a remainder of 2.
The number 2 becomes the next digit in our result. 
Result so far: 86395.2
If we subtract 18 from 20, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 8:
9 can be fit into 20 2 times, resulting in a remainder of 2.
The number 2 becomes the next digit in our result. 
Result so far: 86395.22
Subtracting 18 from 20 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

After the division, we end up with 86395.22 and a remainder of 0.002.