Question

How many rational numbers lie between $\frac{2}{5}$ and $\frac{6}{5}$? [3 MARKS]

Answer 1

Concept :2 Marks
Result : 1 Mark

There are infinite numbers of rational numbers that lie between two points on a number line.

Consider the rational numbers $\frac{2}{5}$ and $\frac{6}{5}$. Take the average of two numbers $\frac{2+6}{5\times 2}$ = $\frac{8}{10}$

$\frac{8}{10}$ lies in the middle of $\frac{2}{5}$ and $\frac{6}{5}$.

Now take the average of $\frac{2}{5}$ and $\frac{8}{10}$. It is $(\frac{2}{5}+\frac{8}{10})\times \frac{1}{2}$ = $\frac{4+8}{10}\times \frac{1}{2}$ = $\frac{12}{20}$

So, as we proceed in this, we will get an infinite number of rational number between two points.