Question

Find four rational numbers between 2 and 3.

Answer 1

Hint: Multiply the given numbers with 10/10 so that they become \[\dfrac{20}{10}\] and \[\dfrac{30}{10}\]. Now, write any four numbers that lie between 20 and 30 and divide each of them by 10 to get four rational numbers.

Complete step-by-step solution
Here, we have to find four rational numbers between 2 and 3. First, let us know about rational numbers.
In mathematics, a rational number is a number that can be expressed as the fraction \[\dfrac{p}{q}\] of two integers, a numerator p and a non – zero denominator q. Since q may be equal to 1, therefore every integer is a rational number. Some examples of rational numbers are: - \[\dfrac{2}{5},\dfrac{3}{8},2,99\] etc.
Now, let us come to the question. Here we have been provided with two rational numbers 2 and 3. We have to find four rational numbers such that they lie between 2 and 3. So, multiplying 2 and 3 with \[\dfrac{10}{10}\], we get,
\[\Rightarrow 2=2\times \dfrac{10}{10}=\dfrac{20}{10}\]
\[\Rightarrow 3=3\times \dfrac{10}{10}=\dfrac{30}{10}\]
Clearly, we can see that the simplified form of \[\dfrac{20}{10}\] and \[\dfrac{30}{10}\] are 2 and 3 respectively, so the numbers did not change.
Now, four numbers between 20 and 30 can be: - 21, 22, 23 and 24. Dividing each of the four numbers by 10, we get, \[\dfrac{21}{10},\dfrac{22}{10},\dfrac{23}{10}\] and \[\dfrac{24}{10}\]. Clearly, we can see that these four fractions obtained are rational numbers and they lie between \[\dfrac{20}{10}\] and \[\dfrac{30}{10}\].
Hence, four rational numbers between 2 and 3 are: - \[\dfrac{21}{10},\dfrac{22}{10},\dfrac{23}{10}\] and \[\dfrac{24}{10}\].

Note: One may note that multiplying 2 and 3 with \[\dfrac{10}{10}=1\] does not change the numbers. Now, I is not necessary to multiply the given numbers with \[\dfrac{10}{10}\], you may also take bigger numbers like \[\dfrac{20}{20},\dfrac{50}{50}\] or \[\dfrac{100}{100}\] etc. Here, we were required to find only four rational numbers and that is why we took \[\dfrac{10}{10}\]. If we were required to find 10 or more rational numbers then we would have taken bigger numbers.