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Question

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

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Solution

## 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,Rational number between $3$ and $4$ is $mean\left(3,4\right)=\frac{\left(3+4\right)}{2}=\frac{7}{2}$Rational number between $3$ and $\frac{7}{2}$ is $mean\left(3,\frac{7}{2}\right)=\frac{\left(3+\frac{7}{2}\right)}{2}=\frac{13}{4}$Rational number between $3$ and $\frac{13}{4}$ is $mean\left(3,\frac{13}{4}\right)=\frac{\left(3+\frac{13}{4}\right)}{2}=\frac{25}{8}$Rational number between $\frac{7}{2}$ and $4$ is $mean\left(\frac{7}{2},4\right)=\frac{\left(\frac{7}{2}+4\right)}{2}=\frac{15}{4}$Rational number between $\frac{15}{4}$ and $4$ is $mean\left(\frac{15}{4},4\right)=\frac{\left(\frac{15}{4}+4\right)}{2}=\frac{31}{8}$Hence, the five rational numbers between $3$ and $4$ are $\frac{7}{2},\frac{13}{4},\frac{15}{4},\frac{25}{8}$ and $\frac{31}{8}$.

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