Question

# Find three rational numbers lying between $0$ and $0.1$. Find twenty rational numbers between $0$ and $0.1$. Give a method to determine any number of rational numbers between $0$ and $0.1$.

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Hint: The above question is based on rational numbers. We have to find out the rational numbers lying between any two numbers. Discuss the basic concept of rational numbers then we can find out the way to solve them. To find the numbers, multiply the given number by $100$ and then by $1000$. In this way, we can conclude our result. Let’s have some more discussion about the same.

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 $\dfrac{{20}}{{1000}}$.
In this way, we found out twenty rational numbers between $0$ and $0.1$.

Note: The above problem can be solved by multiplying the numbers and making $\dfrac{p}{q}$ form. In this way, we can find out infinite rational numbers lying between $0$ and $0.1$. Rational numbers are used for buying and selling products. Real life example of that is sharing a pizza and coke among people.