Question

List five rational numbers between $ - 1$ and $0.$

Answer 1

Hint : Obtain fractions between $ - 1$ and $0.$

As we know rational numbers are those which can be expressed in the form $\dfrac{p}{q}$.
Where q is not equal to zero.
Therefore the rational number between two numbers say a and b can be obtained by doing the operation $\dfrac{{{\text{a + b}}}}{2}$.
Therefore the rational number between -1 and 0 is
$\dfrac{{ - 1 + 0}}{2}$=$\dfrac{{ - 1}}{2}$
The rational number between -1 and $\dfrac{{ - 1}}{2}$ is
$\dfrac{{ - 1 + \dfrac{{ - 1}}{2}}}{2} = \dfrac{{ - 3}}{4}$
The rational number between -1 and $\dfrac{{ - 3}}{4}$ is
$\dfrac{{ - 1 + \dfrac{{ - 3}}{4}}}{2} = \dfrac{{ - 7}}{8}$
The rational number between -1 and $\dfrac{{ - 7}}{8}$ is
$\dfrac{{ - 1 + \dfrac{{ - 7}}{8}}}{2} = \dfrac{{ - 15}}{{16}}$
The rational number between -1 and $\dfrac{{ - 15}}{{16}}$ is
$\dfrac{{ - 1 + \dfrac{{ - 15}}{{16}}}}{2} = \dfrac{{ - 31}}{{32}}$
Therefore the 5 rational numbers between -1 & 0 are

$\dfrac{{ - 1}}{2}$,$\dfrac{{ - 3}}{4}$,$\dfrac{{ - 7}}{8}$,$\dfrac{{ - 15}}{{16}}$,$\dfrac{{ - 31}}{{32}}$.

Note :In mathematics, a rational number is a number that can be expressed as the quotient or fraction $\dfrac{p}{q}$ of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number.