Question

Find 3 rational numbers between 0 and 1.
(a)$\dfrac{3}{2},\dfrac{1}{4}\ \text{and}\ \dfrac{3}{4}$
(b)$\dfrac{1}{2},\dfrac{1}{4}\ \text{and}\ \dfrac{3}{4}$
(c)$\dfrac{1}{2},\dfrac{5}{4}\ \text{and}\ \dfrac{3}{4}$
(d)$\dfrac{1}{2},\dfrac{1}{4}\ \text{and}\ \dfrac{7}{4}$

Answer 1

Hint: Here, we are asked to find a rational number lying between 0 and 1 i.e. $\dfrac{p}{q}$ form where $q\ne 0$. When dividing it lies between 0 and 1. We can start by taking the mid-term between 0 and 1.

Complete step-by-step answer:
In mathematics, a rational number is a number that can be in fraction $\dfrac{p}{q}$ for having non-zero denominator. This type of number either terminates after an infinite number of digits or keeps repeating itself after certain digits.
Now, here rational number between 0 and 1
 $=\dfrac{1}{2}\left( 0+1 \right)\Rightarrow \dfrac{1}{2}$ …………………………………….(i)
$\therefore \dfrac{1}{2}$ is the middle rational number lying between 0 and 1.
$\therefore 0<\dfrac{1}{2}<1$
Now, taking 0 and $\dfrac{1}{2}$, and again finding the middle rational no. so,
 $=\dfrac{1}{2}\left( 0+1 \right)$
$=\dfrac{1}{4}$ ………………………………………..(2)
$0<\dfrac{1}{4}<\dfrac{1}{2}$ where $\dfrac{1}{4}$ is lying between 0 and $\dfrac{1}{2}$.
Similarly, taking $\dfrac{1}{2}$ and 1 number and finding middle rational no.
$=\dfrac{1}{2}\left( \dfrac{1}{2}+1 \right)$
$=\dfrac{1}{2}\left( \dfrac{1+2}{2} \right)$ ……………………………..(iii)
$\therefore \dfrac{3}{4}$ lies between $\dfrac{1}{2}<\dfrac{3}{4}<1$
Thus, we got 3 rational number lying between 0 and 1 which are $\dfrac{1}{2},\dfrac{1}{4},\dfrac{3}{4}$
Hence, option (b) is the correct answer.

Note: Students can find rational numbers by the above shown method or else direct by taking option and can see which option value lies between 0 and 1.
Taking option (a): $\dfrac{3}{2},\dfrac{1}{4},\dfrac{3}{4}$
On dividing this fraction and getting the result in decimal form, we get $1.5,0.25,0.75$.
So, option (a) is not correct as 1.5 does not lie between 0 and 1.
Similarly, option (b): $\dfrac{1}{2},\dfrac{1}{4},\dfrac{3}{4}$
$=0.5,0.25,0.75$
Option (c): $\dfrac{1}{2},\dfrac{5}{4},\dfrac{3}{4}=0.5,\ 1.25,\ 0.75$
Option (d): $\dfrac{1}{2},\dfrac{1}{4},\dfrac{7}{4}=0.5,\ 0.25,\ 1.75$
Hence, option (b) is correct.