Question

Find the rational number between \[1.3\] and \[1.4\] ?

Answer 1

Hint: To find a single rational number between any two numbers we first take the numbers and add them and after adding them we divide it by \[2\] as it form the average which is always a middle number between any two numbers.
Rational number \[=\dfrac{p+q}{2}\]
where \[p\] and \[q\] are the numbers in between which the rational numbers are written.
The rational number can be either in decimal or fraction but here we use decimal as decimal is given in the question.

Complete step-by-step answer:
Rational numbers are numbers in mathematics, where the numbers formed in fractional form can be either negative or positive and the denominator can’t be zero. When written in decimal, numbers after decimal should be finite and not infinite like \[\pi \] as such numbers are called irrationals or irrational numbers.
Now let us get into the question where the two numbers are taken as \[1.3\] and \[1.4\] .
Placing the numbers in the formula to find the rational number as:
Rational number \[=\dfrac{p+q}{2}\]
With \[p=1.3\] or \[p=\dfrac{13}{10}\] and \[q=1.4\] or \[q=\dfrac{14}{10}\] , the value is:
Rational number \[=\dfrac{1.3+1.4}{2}\]
 \[\Rightarrow \dfrac{1.3+1.4}{2}\]
 \[\Rightarrow \dfrac{2.7}{2}\]
 \[\Rightarrow 1.35\]
Hence, one of the rational numbers between the two numbers \[1.3\] and \[1.4\] is \[1.35\] .
So, the correct answer is “ \[1.35\] .”.

Note: Another method to solve the question is by adding a definite number with the first number. We take \[1.3\] and \[1.4\] as \[p\] and \[q\] respectively and another variable which tells us the number of rational numbers we need to find let us take it as \[n\] . The formula to find the rational number is:
 \[p+d\] with \[d=\dfrac{q-p}{n+1};q>p\] .
Placing the values in the formula, we get the value of \[d\] as:
 \[\Rightarrow \dfrac{q-p}{n+1}\]
 \[\Rightarrow \dfrac{1.4-1.3}{1+1}\]
 \[\Rightarrow \dfrac{1}{20}\]
After this we add the value by \[p\] to get the rational number as \[p+d\] :
 \[\Rightarrow 1.3+0.05\]
 \[\Rightarrow 1.35\]