Question

Find two rational numbers between $ 0.1 $ and $ 0.3 $

Answer 1

Hint: To find the rational numbers between two numbers convert the numbers in $ p/q $ form where q is not equal to zero. Thus every rational number has a numerator and a denominator.

Complete step-by-step answer:
Rational number is a number that can be expressed as quotient or fraction $ p/q $ of two integers, a numerator p and a non-zero denominator q. Example of a rational number is $ -3/7 $ .
Every integer is a rational number.
Since a rational number is the subset of the real number, it will obey all the properties of real numbers.
The rational numbers between two rational number can be found easily using two different methods:
Find out the equivalent fraction of the given rational number and find out rational numbers in between them.
Find out the mean value of the two given rational numbers, the mean value obtained is the required rational number.
Formula for finding the rational number is $ \dfrac{a+b}{2} $ . Where ‘a’ is the first number and ‘b’ is the second number (Mean method).
Here $ a=0.1 $ and $ b=0.3 $
Using the above from formula we get :-
 $ \dfrac{a+b}{2}=\dfrac{0.1+0.3}{2} $
 $
   =\dfrac{0.4}{2} \\
  =0.2 \;
 $
Hence, one rational number between $ 0.1 $ and $ 0.3 $ is $ 0.2 $ .
To find the second rational no. We will use the above formula between $ 0.2 $ and $ 0.3 $ . You can also find the rational number between $ 0.1 $ and $ 0.2 $
Therefore,
 $
  a=0.2 \\
  b=0.3 \\
 $
  $ \dfrac{a+b}{2}=\dfrac{0.2+0.3}{2} $
 $
   =\dfrac{0.5}{2} \\
  =0.25 \;
 $
So, two rational between $ 0.1 $ and $ 0.3 $ are $ 0.2 $ and $ 0.25 $
So, the correct answer is “$ 0.2 $ and $ 0.25 $ ”.

Note: You can also find the rational numbers by converting them in p/q form.
 $
   0.1=\dfrac{10}{100} \\
  0.3=\dfrac{30}{100} \;
 $
Therefore, rational numbers are $ \dfrac{11}{100},\dfrac{12}{100},......\dfrac{20}{100},......\dfrac{25}{100},....\dfrac{30}{100} $
There are many rational numbers between two numbers.