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

Respuesta :

Answer:

The reciprocal of n must be less than 10.

Step-by-step explanation:

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

But,

[tex](n)^{2}[/tex] < [tex]\frac{1}{100}[/tex]

Find the square root of both sides,

n < [tex]\sqrt{\frac{1}{100} }[/tex]

⇒ n < [tex]\frac{1}{10}[/tex]

n < 0.1

The reciprocal of n can be estimated as;

[tex](n)^{-1}[/tex] < [tex](\frac{1}{10}) ^{-1}[/tex]

[tex]\frac{1}{n}[/tex] < 10

The reciprocal of n is less than 10.