2. Visual representation of rational numbers between two rational numbers

If we want to find more number of rational numbers between two numbers, then we should find the multiples of the rational numbers given.

For example, if we want to find more number of rational numbers between  $\frac{3}{5}\mathit{and}\frac{4}{5}$. We should write the multiple of the rational numbers, that is,

 

This can be better understood by representing in a number line,

 

 

We can find even more number of rational numbers between $\frac{3}{5}\mathit{and}\frac{4}{5}$ by writing the multiple of a rational number as $\frac{300}{500}\mathit{and}\frac{400}{500}$. Now, there are \(100\) rational numbers present between $\frac{3}{5}\mathit{and}\frac{4}{5}$.

 

From, this we can understand that an infinite (or) an uncountable number of rational numbers are present between any two rational numbers.

 

This is one of the methods to find rational numbers between any two rational numbers. There is another method to find rational numbers between any two rational numbers using the average concept which is explained in the upcoming lesson.