Question

Find five Rational numbers between $1$ and $2$.

Answer 1

Compute the required rational numbers:

A rational number can be defined as, any number which can be expressed in the form of $\frac{p}{q}$ where $q\ne 0$.

Given two numbers are $1$ and $2$.

We know that the rational number between $a$ and $b$ is obtained by $\frac{\left(a+b\right)}{2}$, so,

1. Rational number between $1$ and $2$ is $\frac{\left(1+2\right)}{2}=\frac{3}{2}$
2. Rational number between $1$ and $\frac{3}{2}$is $\frac{\left(1+{\displaystyle \frac{3}{2}}\right)}{2}=\frac{5}{4}$
3. Rational number between $1$ and $\frac{5}{4}$ is $\frac{\left(1+{\displaystyle \frac{5}{4}}\right)}{2}=\frac{9}{8}$
4. Rational number between $2$ and $\frac{3}{2}$ is $\frac{\left(2+{\displaystyle \frac{3}{2}}\right)}{2}=\frac{7}{4}$
5. Rational number between $2$ and $\frac{7}{4}$ is $\frac{\left(2+{\displaystyle \frac{7}{4}}\right)}{2}=\frac{15}{8}$

Hence, the five rational numbers between $1$ and $2$ are $\frac{3}{2}$, $\frac{5}{4}$,$\frac{9}{8}$,$\frac{7}{4}$ and $\frac{15}{8}$.