Question

Find five rational numbers between $3$ and $4$.

Answer 1

Compute the required rational numbers :

We can obtain the rational number between $a$ and $b$ using the mean method as $mean\left(a,b\right)=\frac{\left(a+b\right)}{2}$, so,

1. Rational number between $3$ and $4$ is $mean\left(3,4\right)=\frac{\left(3+4\right)}{2}=\frac{7}{2}$
2. Rational number between $3$ and $\frac{7}{2}$ is $mean\left(3,\frac{7}{2}\right)=\frac{\left(3+{\displaystyle \frac{7}{2}}\right)}{2}=\frac{13}{4}$
3. Rational number between $3$ and $\frac{13}{4}$ is $mean\left(3,\frac{13}{4}\right)=\frac{\left(3+{\displaystyle \frac{13}{4}}\right)}{2}=\frac{25}{8}$
4. Rational number between $\frac{7}{2}$ and $4$ is $mean\left(\frac{7}{2},4\right)=\frac{\left({\displaystyle \frac{7}{2}}+4\right)}{2}=\frac{15}{4}$
5. Rational number between $\frac{15}{4}$ and $4$ is $mean\left(\frac{15}{4},4\right)=\frac{\left({\displaystyle \frac{15}{4}}+4\right)}{2}=\frac{31}{8}$

Hence, the five rational numbers between $3$ and $4$ are $\frac{7}{2},\frac{13}{4},\frac{15}{4},\frac{25}{8}$ and $\frac{31}{8}$.