90101 ÷ 9 = 10011 R2
Alright, let's work through the division of 90101 by 9 step by step.

Step 1:
9 goes into 9 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 9 from 9 to get 0.
Bring next digit (0) of the dividend behind the 0 and repeat the process: 0 / 9

Step 2:
9 goes into 0 0 times with a remainder of 0.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 0 to get 0.
Bring next digit (1) of the dividend behind the 0 and repeat the process: 1 / 9

Step 3:
9 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 100
Subtract 0 from 1 to get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 9

Step 4:
9 goes into 10 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 1001
Subtract 9 from 10 to get 1.
Bring next digit (1) of the dividend behind the 1 and repeat the process: 11 / 9

Step 5:
9 goes into 11 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 10011
Subtract 9 from 11 to get 2.

The final result is 10011 with a remainder of 2.