Question

Insert two rational numbers between 1 and 2.

Answer 1

Hint: Rational numbers are the m numbers which can be expressed in the form $ \dfrac{p}{q}$ . Where q is not equal to zero.
There are infinite rational numbers between two rational numbers. To insert a rational number between two numbers we can take the average of thr numbers.

Complete step-by-step solution:
Finding the rational numbers between two numbers.
In our case we have given the numbers 1 and 2
To find the rational numbers between 1 and 2 we can take the average of both the numbers
$ \Rightarrow \dfrac{{1 + 2}}{2} = \dfrac{3}{2}$
We can call $ \dfrac{3}{2}$ as the first rational number found.
Now in the next step we can find out the rational numbers between 1 and 1.5 or 1.5 and 2
We have to take the average of those two numbers.
$ \Rightarrow \dfrac{{1 + \dfrac{3}{2}}}{2} = \dfrac{5}{4}$
So the two rational numbers found between 1 and 2 are $ \dfrac{3}{2},\dfrac{5}{4}$

Note: We can actually find out infinite numbers in between 1 and 2. Instead of taking average we can divide by 3,4,… etc. Following the process on and on will give us infinite rational numbers between the numbers given in the question.