QUESTION

# Find the five rational numbers between 3 and 4.

Hint: The rational number between a and b is $\dfrac{{(a + b)}}{2}$, use this equation to find the rational numbers between the given two numbers. Rational numbers are the numbers which can be written as $\dfrac{p}{q}$ where p and q are integers and q≠0.
As, we know, the rational number between a and b is given by, $\dfrac{{(a + b)}}{2}$
Hence, the rational number between 3 and 4 is $\dfrac{{(3 + 4)}}{2} = \dfrac{7}{2} = 3.5$
Rational number between 3 and 7/2 is $\left[ {\dfrac{{3 + \left( {\dfrac{7}{2}} \right)}}{2}} \right] = \dfrac{{13}}{4} = 3.25$
Rational number between 3 and 13/4 is $\left[ {\dfrac{{3 + \left( {\dfrac{{13}}{4}} \right)}}{2}} \right] = \dfrac{{25}}{8} = 3.125$
Rational number between 3 and 25/8 is $\left[ {\dfrac{{3 + \left( {\dfrac{{25}}{8}} \right)}}{2}} \right] = \dfrac{{49}}{{16}} = 3.0625$
Rational number between 25/8 and 2 is $\left[ {\dfrac{{\left( {\dfrac{{25}}{8}} \right) + 4}}{2}} \right] = \dfrac{{57}}{{16}} = 3.5625$