Question

Find the four rational numbers between 1 and 2.

Answer 1

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.

Complete step-by-step answer:
Here we have to find 4 rational numbers between 1 and 2.
As, we know, the rational number between a and b is given by, $\dfrac{{(a + b)}}{2}$
Hence, the rational number between 1 and 2 is $\dfrac{{(1 + 2)}}{2} = \dfrac{3}{2} = 1.5$
Rational number between 1 and 3/2 is $\left[ {\dfrac{{1 + \left( {\dfrac{3}{2}} \right)}}{2}} \right] = \dfrac{5}{4} = 1.25$
Rational number between 1 and 5/4 is $\left[ {\dfrac{{1 + \left( {\dfrac{5}{4}} \right)}}{2}} \right] = \dfrac{9}{8} = 1.125$
Rational number between 3/2 and 2 is $\left[ {\dfrac{{\left( {\dfrac{3}{2}} \right) + 2}}{2}} \right] = \dfrac{7}{4} = 1.75$
Therefore, four rational numbers between 1 and 2 are 9/8, 5/4, 3/2, and 7/4.

Note: Whenever such a type of question appears, i.e., it is asked to find a rational number between any two rational numbers, suppose x and y, the simplest approach is to divide their sum by 2, as mentioned in the question. Proceed step by step, obtain the value of (sum of the two no.)/2, then find the next rational number by dividing the sum of the first rational no. obtained in step 1 with the first number in the range, repeat it till you get all the required rational numbers.