Question

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

Answer 1

Rational number is any number that can express in the form of $\frac{p}{q}$ of two integers, where '$q$' cannot be zero.

i) First rational number between $3$ and $4$ can be calculated by finding average between them, which is

$\frac{3+4}{2}=\frac{7}{2}$

Now, we have three numbers i.e. $3,\frac{7}{2}$ and $4$, so other remaining rational numbers can be calculated by taking average between $3$ and $\frac{7}{2}$, and between $\frac{7}{2}$ and $4$.

ii) Second rational number between $3$ and $\frac{7}{2}$ can be calculated by finding average between them.

$\frac{\frac{7}{2}+3}{2}=\frac{\frac{7+6}{2}}{2}=\frac{13}{4}$

iii) The third rational number between $4$ and $\frac{7}{2}$ can be calculated by finding the average between them.

$\frac{\frac{7}{2}+4}{2}=\frac{\frac{7+8}{2}}{2}=\frac{15}{4}$

iv) Similarly fourth rational number between $3$ and $\frac{13}{4}$ can be calculated by finding the average between them.

$\frac{\frac{13}{4}+3}{2}=\frac{\frac{13+12}{4}}{2}=\frac{25}{8}$

v) Similarly, fifth rational number between $4$ and $\frac{13}{4}$ can be calculated by finding average between them.

$\frac{\frac{13}{4}+4}{2}=\frac{\frac{13+16}{4}}{2}=\frac{29}{8}$

Then the rational numbers between $3$ and $4$ are

$\frac{7}{2},\frac{13}{4},\frac{15}{4},\frac{25}{8},\frac{29}{8}$