Question

what rational numbers lies between 1/10 and 9/4 ?​

Answer 1

To find:

Rational numbers that lie between $\dfrac{1}{10}$ and $\dfrac{9}{4}$

Step-by-step explanation:

The denominators of $\dfrac{1}{10}$ and $\dfrac{9}{4}$ are $10$ and $4$ respectively.

Here, LCM of $10$ and $4$ is $20$ and thus we can write the given fractions as follows,

• $\dfrac{1}{10}=\dfrac{1\times 2}{10\times 2}=\dfrac{2}{20}$

• $\dfrac{9}{4}=\dfrac{9\times 5}{4\times 5}=\dfrac{45}{20}$

Since there can be infinite number of rational numbers between two rational numbers, we can also conclude the same for $\dfrac{2}{20}$ and $\dfrac{45}{20}$.

Examples: Some rational numbers between $\dfrac{2}{20}$ and $\dfrac{45}{20}$ are

$\quad \dfrac{3}{20},\dfrac{4}{20},\dfrac{5}{20},\dfrac{6}{20},...\:...,\dfrac{44}{20}$

Final answer:

There are infinite number of rational numbers between $\dfrac{1}{10}$ and $\dfrac{9}{4}$, some of which are

$\quad \dfrac{3}{20},\dfrac{4}{20},\dfrac{5}{20},\dfrac{6}{20},...\:...,\dfrac{44}{20}$.