yvonne12 wrote:if N denotes a number to the left of 0 on the number line such that the square of N is less than that the square of N is less than 1/100, then the recipricol of N must be

less than -10
between -1 and -1/10
between -1/10 and 0
between 0 and 1/10
greater than 10

We are given that N denotes a number to the left of 0 on the number line such that the square of N is less than 1/100. This means N is negative, and it is between 0 and -1/10 since (-1/10)^2 = 1/100. Thus, N could be equal to values such as -1/11, -1/12, -1/13, etc. Notice that when we square these values, they are all less than 1/100.

Let's take the reciprocal of any of these values listed. The reciprocal of -1/11 is -11. Similarly, the reciprocal of -1/12 is -12, and the reciprocal of -1/13 is -13. Since these reciprocals are all less than -10, answer choice A is correct.

Alternate Solution:

Let's find a value for N such that N is negative and the square of N is less than 1/100. If we take N = -1/20, we see that N^2 = 1/400, which is less than 1/100. Now, the reciprocal of N is 1/N = -20, which is less than -10.

Answer: A