Question

how many rational numbers are there which are equal to their reciprocals? show how

Answer 1

A rational number is the one which can be written in p/q form

Its reciprocal is q/p

For both of them to be equal, the number must be1

Only 1 is the rational numbers which equals its reciprocal

Answer 2

It has infinite numbers are there between the rational number and their reciprocals.

Example :
suppose 2/3 is the rational we took
so numbers between 2/3 and its reciprocal 3/2 is
= 2/3              3/2
=4/6               9/6
=0.33...           1.5
between numbers are
0.4,0.5,0.6,.7,0.8,0.9,1.0, 1.1, 1.2, 1.3, 1.4, 
0.41, 0.51, 0.61, 0.71.........