645841 ÷ 9 
Our goal is to divide 645841 by 9.

Moving on to step 1:
6 divided by 9 is 0 with a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 6 after subtracting 0 from 6.
Take the next digit (4) from the dividend and append it to 6, then repeat: 64 / 9

Going ahead to step 2:
64 divided by 9 is 7 with a remainder of 1.
The number 7 becomes the next digit in our result. 
Result so far: 7.0
If we take 63 away from 64, we end up with 1.
Include the next digit (5) from the dividend after 1, then repeat: 15 / 9

Moving on to step 3:
The number 9 fits into 15 1 times, leaving a remainder of 6.
Use 1 as the next digit of our solution. 
Result so far: 71.0
If we subtract 9 from 15, we get 6.
Append the next digit (8) from the dividend to 6 and continue with: 68 / 9

Step 4:
9 goes into 68 7 times with a remainder of 5.
Write down 7 as next digit of the result. 
Result so far: 717.0
If we subtract 63 from 68, we get 5.
Grab the next digit (4) from the dividend, add it to 5, then carry on: 54 / 9

Going ahead to step 5:
9 goes into 54 6 times with a remainder of 0.
Put 6 as the next digit of the answer. 
Result so far: 7176.0
Subtracting 54 from 54 leaves us with 0.
Bring next digit (1) of the dividend behind the 0 and repeat the process: 1 / 9

Moving on to step 6:
9 goes into 1 0 times with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 71760.0
Deduct 0 from 1 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Advancing to step 7:
If we divide 10 by 9, we get 1 and a remainder of 1.
Write down 1 as next digit of the result. 
Result so far: 71760.1
Deduct 9 from 10 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 8:
When dividing 10 by 9, we get 1 with a remainder of 1.
Use 1 as the next digit of our solution. 
Result so far: 71760.11
The remainder is 1 after subtracting 9 from 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

The final outcome is 71760.11, with a leftover of 0.001.