Data Sufficiency

If n is a positive integer that is less than 10, what is the value of n?
(1) n is the tenth digit in the decimal representation of 1/n.
(2) n is the hundredth digit in the decimal representation of 1/n.

1/2=0.5
1/3=0.33
1/4=0.25
1/5=0.2
1/6=0.167
1/7=0.143
1/8=0.125
1/9=0.111

Therefore, from (1), tenth digit in the decimal representation above could be 5,3,2, and 1. So, insufficient.
from (2), hundreth digit could be 3, 5, 6,4,3,1. So, insufficient.
So, I chose E. But, correct answer is A. What am I doing wrong?

the statement 1 says value of 1/n = 0.n.....

which can happen only if n =3 hence suff

stmt 2 says

value of 1/n = o.?n....

which can happen for n = 3 or n =6 hence Insuff