n^2 < 1/100 means that n is between -1/10 and 1/10. Since n is on the left of zero on the number line, this means that n is between -1/10 and 0:
-1/10 < n < 0. Finding the reciprocal means flipping the "<" into ">", but since n is negative, the ">" will be flipped again back to "<":

1/(-1/10) < 1/n < 0
-10 < n < 0.

n<1/100
=>n<1/10 or n>-1/10

since n<0, n must lie between -1/10 and 0

reciprocal of n would be between -10 and infinity
=> less than -10


hence A

n < 0 & n^2 < 1/100... n < - 1/10

Multiplying both sides by -10 while dividing by n

-10 > 1/n

Therefore A