6. 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 \(\frac{3}{5}\) and \(\frac{4}{5}\). We should write the multiple of the rational numbers, that is, \(\frac{3}{5}\) can be written as \(\frac{30}{50}\) and \(\frac{4}{5}\) can be written as \(\frac{40}{50}\).

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

 

 

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