9106 ÷ 90 
We're looking to find how many times 90 goes into 9106.

On to step 1:
If we divide 9 by 90, we get 0 and a remainder of 9.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 9 to get 9.
Take the next digit (1) from the dividend and append it to 9, then repeat: 91 / 90

On to step 2:
90 goes into 91 1 times with a remainder of 1.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Deduct 90 from 91 and we're left with 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 90

Going ahead to step 3:
If we divide 10 by 90, we get 0 and a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 10.0
The remainder is 10 after subtracting 0 from 10.
Grab the next digit (6) from the dividend, add it to 10, then carry on: 106 / 90

On to step 4:
When dividing 106 by 90, we get 1 with a remainder of 16.
The number 1 becomes the next digit in our result. 
Result so far: 101.0
Subtracting 90 from 106 leaves us with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Step 5:
When dividing 160 by 90, we get 1 with a remainder of 70.
Record the quotient 1 as the next digit in the result. 
Result so far: 101.1
Deduct 90 from 160 and we're left with 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Moving on to step 6:
700 divided by 90 is 7 with a remainder of 70.
The next digit of our result is 7. 
Result so far: 101.17
If we take 630 away from 700, we end up with 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Going ahead to step 7:
The number 90 fits into 700 7 times, leaving a remainder of 70.
Write down 7 as next digit of the result. 
Result so far: 101.177
The remainder is 70 after subtracting 630 from 700.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Our division results in 101.177 with a remaining 0.007.