Question

If n denotes a number to the left of 0 on the number line such that the square of n is less than \small \frac{1}{100}, then the reciprocal of n must be

Answer 1

The reciprocal of n must be less than 10.

Explanation:

It can be inferred from the question given that n is not a negative number.

But,

`(n)^(2)` <
`(1)/(100)`

Find the square root of both sides,

n <
`\sqrt{(1)/(100) }`

⇒ n <
`(1)/(10)`

n < 0.1

The reciprocal of n can be estimated as;

`(n)^(-1)` <
`((1)/(10)) ^(-1)`

`(1)/(n)` < 10

The reciprocal of n is less than 10.