Question

There are infinitely many rational numbers between any two rational numbers

• A. True
• B. False

Answer 1

The correct option is A

True

The statement is True.

Consider the rational numbers 3 and 5

we have $\frac{3}{1}$ and $\frac{5}{1}$ where $\frac{3}{1}$ < $\frac{5}{1}$

$\Rightarrow$ $\frac{3}{1}<\frac{3+5}{1+1}<\frac{5}{1}$ = $\frac{3}{1}<\frac{4}{1}<\frac{5}{1}$

$\Rightarrow$ $\frac{3}{1}<\frac{3+4}{1+1}<\frac{4}{1}$ < $\frac{4+5}{1+1}<\frac{5}{1}<\frac{5}{1}$

$\Rightarrow$ 3 < $\frac{7}{2}<4<\frac{9}{2}<5$ i.e 3 < $3\frac{1}{2}<4<4\frac{1}{2}<5$

Also every terminating and non -terminating recurring decimal number between 3 and 5 is a rational number

For example (i) 3.2 < 3.85 < 4.3