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 ${\displaystyle \frac{p}{q}}$.
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 ${\displaystyle \frac{\text{a + b}}{2}}$.
Therefore the rational number between -1 and 0 is
${\displaystyle \frac{-1+0}{2}}$=${\displaystyle \frac{-1}{2}}$
The rational number between -1 and ${\displaystyle \frac{-1}{2}}$ is
${\displaystyle \frac{-1+{\displaystyle \frac{-1}{2}}}{2}}={\displaystyle \frac{-3}{4}}$
The rational number between -1 and ${\displaystyle \frac{-3}{4}}$ is
${\displaystyle \frac{-1+{\displaystyle \frac{-3}{4}}}{2}}={\displaystyle \frac{-7}{8}}$
The rational number between -1 and ${\displaystyle \frac{-7}{8}}$ is
${\displaystyle \frac{-1+{\displaystyle \frac{-7}{8}}}{2}}={\displaystyle \frac{-15}{16}}$
The rational number between -1 and ${\displaystyle \frac{-15}{16}}$ is
${\displaystyle \frac{-1+{\displaystyle \frac{-15}{16}}}{2}}={\displaystyle \frac{-31}{32}}$
Therefore the 5 rational numbers between -1 & 0 are

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

Note :In mathematics, a rational number is a number that can be expressed as the quotient or fraction ${\displaystyle \frac{p}{q}}$ 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.