959631 divided by 9 
We want to figure out the number of times 959631 can be divided by 9.

Going ahead to step 1:
9 can be fit into 9 1 times, resulting in a remainder of 0.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Deduct 9 from 9 and we're left with 0.
Include the next digit (5) from the dividend after 0, then repeat: 5 / 9

Moving on to step 2:
The number 9 fits into 5 0 times, leaving a remainder of 5.
The next digit of our result is 0. 
Result so far: 10.0
If we take 0 away from 5, we end up with 5.
Take the next digit (9) from the dividend and append it to 5, then repeat: 59 / 9

Advancing to step 3:
9 can be fit into 59 6 times, resulting in a remainder of 5.
The number 6 becomes the next digit in our result. 
Result so far: 106.0
If we take 54 away from 59, we end up with 5.
Grab the next digit (6) from the dividend, add it to 5, then carry on: 56 / 9

Step 4:
When dividing 56 by 9, we get 6 with a remainder of 2.
Write down 6 as next digit of the result. 
Result so far: 1066.0
Subtract 54 from 56 to get 2.
Grab the next digit (3) from the dividend, add it to 2, then carry on: 23 / 9

Step 5:
9 can be fit into 23 2 times, resulting in a remainder of 5.
The number 2 becomes the next digit in our result. 
Result so far: 10662.0
Subtract 18 from 23 to get 5.
Append the next digit (1) from the dividend to 5 and continue with: 51 / 9

Let's proceed to step 6:
9 can be fit into 51 5 times, resulting in a remainder of 6.
Record the quotient 5 as the next digit in the result. 
Result so far: 106625.0
Subtract 45 from 51 to get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Advancing to step 7:
If we divide 60 by 9, we get 6 and a remainder of 6.
The number 6 becomes the next digit in our result. 
Result so far: 106625.6
If we take 54 away from 60, we end up with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

On to step 8:
If we divide 60 by 9, we get 6 and a remainder of 6.
Record the quotient 6 as the next digit in the result. 
Result so far: 106625.66
If we subtract 54 from 60, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

The final outcome is 106625.66, with a leftover of 0.006.