Question

List five rational numbers between -2 and -1.

Answer 1

Hint: In this question we have to find five rational numbers between the given numbers. A rational number is one which is of the form $\dfrac{p}{q}$ where $q \ne 0$, use this basic definition of rational numbers. Firstly figure out all the decimal integers (only 5 required) then convert them into fractional form to get the answers.

Complete step-by-step answer:
As we know rational numbers are those which are written in the form of $\dfrac{p}{q}$, where $q \ne 0$ and $\dfrac{p}{q}$ is written in lowest form, such that $p$ and $q$ have not no common factors except 1.

For example $\dfrac{2}{3}$ as this fraction is written in lowest form and does not have any common factors except 1, so this is a rational number.

Now we have to find out the rational numbers between -2 and -1 i.e. greater than -2 and less than -1.

So consider any five numbers between -2 and -1 which is $\left\{ { - 1.1, - 1.2, - 1.3, - 1.4, - 1.5} \right\}$

Now, convert these numbers into fraction

$ - 1.1 = \dfrac{{ - 11}}{{10}},{\text{ }} - 1.2 = \dfrac{{ - 12}}{{10}},{\text{ }} - 1.3 = \dfrac{{ - 13}}{{10}},{\text{ }} - 1.4 = \dfrac{{ - 14}}{{10}},{\text{ }} - 1.5 = \dfrac{{ - 15}}{{10}},$

Now, convert these fraction into lowest form such that these fraction have not any common factors

$

   \Rightarrow - 1.1 = - \dfrac{{11}}{{10}} \\

   \Rightarrow - 1.2 = - \dfrac{{12}}{{10}} = - \dfrac{6}{5} \\

   \Rightarrow - 1.3 = - \dfrac{{13}}{{10}} \\

   \Rightarrow - 1.4 = \dfrac{{14}}{{10}} = - \dfrac{7}{5} \\

   \Rightarrow - 1.5 = \dfrac{{15}}{{10}} = - \dfrac{3}{2} \\

$

So, \[\left\{ { - \dfrac{3}{2}, - \dfrac{7}{5}, - \dfrac{{13}}{{10}}, - \dfrac{6}{5}, - \dfrac{{11}}{{10}}} \right\}\] are the required five rational numbers between (-2 and -1).

Note: Whenever we face such types of problems the key concept is simply to have the gist of the basic understanding of rational numbers. There can be many decimal integers between a given interval but however be concerned only about the number of rational numbers being asked, this will help you getting on the right track to reach the answer.