Question

Find two rational numbers between 3 and 4 by mean method.

Answer 1

Hint: To place few rational numbers between a and b, use the mean method. Therefore the rational numbers between a and b will be $\dfrac{{a + b}}{2},\dfrac{{a + \dfrac{{a + b}}{2}}}{2},etc$.

Complete step-by-step answer:
Use the mean method. According to the mean method, finding a rational number between two rational numbers x and y is to divide their sum by 2.
Therefore the rational numbers between a and b will be $\dfrac{{a + b}}{2},\dfrac{{a + \dfrac{{a + b}}{2}}}{2},etc$.
∴ By mean method, two rational numbers between 3 and 4 can be
$\dfrac{{3 + 4}}{2} = \dfrac{7}{2}$ and $\dfrac{{3 + \dfrac{7}{2}}}{2} = \dfrac{{13}}{4}$
Hence, the two rational Numbers between 3 and 4 are \[\dfrac{7}{2}{\text{ }}and{\text{ }}\dfrac{{13}}{4}\]

Note:

 By mean method, two rational numbers between 3 and 4 can be
$\dfrac{{3 + 4}}{2} = \dfrac{7}{2}$ and $\dfrac{{3 + \dfrac{7}{2}}}{2} = \dfrac{{13}}{4}$
 Note that \[3{\text{ }} < \dfrac{{13}}{4} < \dfrac{7}{2} < {\text{ }}4\]
It is the simplest method to find a rational number between two numbers.