655437 ÷ 9 
We're looking to find how many times 9 goes into 655437.

Step 1:
9 goes into 6 0 times with a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 6 to get 6.
Take the next digit (5) from the dividend and append it to 6, then repeat: 65 / 9

Going ahead to step 2:
When dividing 65 by 9, we get 7 with a remainder of 2.
Write down 7 as next digit of the result. 
Result so far: 7.0
The remainder is 2 after subtracting 63 from 65.
Take the next digit (5) from the dividend and append it to 2, then repeat: 25 / 9

Going ahead to step 3:
9 goes into 25 2 times with a remainder of 7.
Write down 2 as next digit of the result. 
Result so far: 72.0
Subtracting 18 from 25 leaves us with 7.
Append the next digit (4) from the dividend to 7 and continue with: 74 / 9

Step 4:
9 goes into 74 8 times with a remainder of 2.
Put 8 as the next digit of the answer. 
Result so far: 728.0
The remainder is 2 after subtracting 72 from 74.
Bring next digit (3) of the dividend behind the 2 and repeat the process: 23 / 9

Advancing to step 5:
When dividing 23 by 9, we get 2 with a remainder of 5.
The number 2 becomes the next digit in our result. 
Result so far: 7282.0
If we take 18 away from 23, we end up with 5.
Take the next digit (7) from the dividend and append it to 5, then repeat: 57 / 9

Advancing to step 6:
When dividing 57 by 9, we get 6 with a remainder of 3.
The next digit of our result is 6. 
Result so far: 72826.0
The remainder is 3 after subtracting 54 from 57.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

On to step 7:
When dividing 30 by 9, we get 3 with a remainder of 3.
Record the quotient 3 as the next digit in the result. 
Result so far: 72826.3
If we take 27 away from 30, we end up with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Let's proceed to step 8:
9 can be fit into 30 3 times, resulting in a remainder of 3.
Put 3 as the next digit of the answer. 
Result so far: 72826.33
Deduct 27 from 30 and we're left with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

The final outcome is 72826.33, with a leftover of 0.003.