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Rational numbers are those which are in the form of $\dfrac{p}{q}$ where a condition is applied that $q$ does not equal to zero.

There are two numbers given i.e. $0$ and $0.1$

Firstly, we have to find out the three rational numbers lying between $0$ and $0.1$.

We have $0$, so we can multiply the term by $\dfrac{1}{{100}}$ and we will get

$0 * \dfrac{1}{{100}} = 0$

We have another number $0.1$, it can be written as $\dfrac{1}{{10}}$. Multiplying the term by $\dfrac{4}{{10}}$, we get:

$\Rightarrow$ $\dfrac{1}{{10}} * \dfrac{4}{{10}} = \dfrac{4}{{100}}$

We get the numbers that are $0$ and $\dfrac{4}{{100}}$

So, the three rational numbers lying between $0$ and $\dfrac{4}{{100}}$ are:

$\dfrac{1}{{100}},\dfrac{2}{{100}},\dfrac{3}{{100}}$

Similarly, we can find the twenty rational numbers by multiplying them.

As we have $0$ and $\dfrac{1}{{10}}$, multiplying $0$ by $\dfrac{1}{{1000}}$ we get

$\Rightarrow$ $0 * \dfrac{1}{{1000}} = 0$

Multiplying $100$ on numerator and denominator of $\dfrac{1}{{10}}$, we get

$ = \dfrac{1}{{10}} * \dfrac{{100}}{{100}}$

$\Rightarrow$ $\dfrac{{100}}{{1000}}$

Now, twenty rational numbers between $0$ and $\dfrac{1}{{10}}$ or we can say between $0$ and $\dfrac{{100}}{{1000}}$ are:

$\dfrac{1}{{1000}},\dfrac{2}{{1000}},\dfrac{3}{{1000}},\dfrac{4}{{1000}},\dfrac{5}{{1000}},\dfrac{6}{{1000}},\dfrac{7}{{1000}},\dfrac{8}{{1000}},\dfrac{9}{{1000}},\dfrac{{10}}{{1000}},\dfrac{{11}}{{1000}},\dfrac{{12}}{{1000}},\dfrac{{13}}{{1000}},\dfrac{{14}}{{1000}},\dfrac{{15}}{{1000}},$

$\dfrac{{16}}{{1000}},\dfrac{{17}}{{1000}},\dfrac{{18}}{{1000}},\dfrac{{19}}{{1000}}$ and $\dfrac{{20}}{{1000}}$.

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