Question

there are innumerable rational number between two rational number true or false ​

Answer 1

Yes true hope it will help you please mark it as brainlist

Answer 2

True, there are infinite rational numbers between two rational numbers.

To understand this, let's suppose we need to find rational numbers between 1/5 and 3/5.

As you can see, we have 2/5 between 1/5 and 3/5 but if we multiply the numerator and denominator of a fraction with same number, it's value doesn't change.

i.e., $\frac{1}{5}$ × $\frac{2}{2}$ = $\frac{2}{10}$ and $\frac{3}{5}$ × $\frac{2}{2}$ = $\frac{6}{10}$

.: By multiplying the numerator and denominator with same number, we are just changing them to their equivalent fractions, which have equal value as the initial fraction.

Now we can add more rational numbers between 2/10 and 6/10 (2/10 = 1/5 and 6/10 = 3/5)

⇒ 3/10, 4/10, 5/10

Similarly, $\frac{1}{5}$ × $\frac{10}{10}$ = $\frac{10}{50}$ and $\frac{3}{5}$ × $\frac{10}{10}$ = $\frac{30}{50}$

Hence, rational numbers between 10/50 and 30/50 are..

⇒ 11/50, 12/50, 13/50,...28/50,29/50

This way we can keep adding more and more rational numbers between two rational numbers by finding their equivalent fraction.