Answer
438k+ views
Hint: First, before proceeding for this, we must know the condition that the rational number is always an integer is not necessary but an integer can be written as a rational number always. Then, rational number is the number of the form $ \dfrac{p}{q} $ where $ q\ne 0 $ and an integer is the number that has an integer value and always comes in total range of number from $ -\infty $ to $ \infty $ .Then, the example considered by us as $ \dfrac{3}{4} $ is not an integer but still a rational number.
Complete step-by-step answer:
In this question, we are supposed to find a number which is rational but not an integer.
So, before proceeding for this, we must know the condition that the rational number is always an integer is not necessary but an integer can be written as a rational number always.
Here, we are said to give an example of the rational number which is not an integer.
But, before that, we all should know what is a rational number.
So, the rational number is the number of the form $ \dfrac{p}{q} $ where $ q\ne 0 $ .
However, an integer is the number that has an integer value and always comes in the total range of numbers from $ -\infty $ to $ \infty $ .
Now, to take an example of any rational number which is not an integer is:
$ \dfrac{3}{4} $
Here, the example considered by us as $ \dfrac{3}{4} $ is not an integer but still a rational number.
Now, to prove that it is not an integer, find the decimal value of the number considered as:
$ \dfrac{3}{4}=0.75 $
So, it gives the value 0.75 and by the definition of integers, it is not an integer value.
But when we go for the definition of rational number, $ \dfrac{3}{4} $ is of form $ \dfrac{p}{q} $ and also its denominator is not zero which states that it is a valid rational number.
Similarly, we can take many numbers which are rational numbers but not integers.
Hence, it is proved that $ \dfrac{3}{4} $ is a rational number but not an integer.
Note: Now, to solve these types of questions, it was not necessary to take this fixed example as $ \dfrac{3}{4} $ to prove that a rational number is not necessarily an integer. So, in mathematics of the numbers, we have a number of rational numbers like $ \dfrac{1}{2},\dfrac{6}{8},\dfrac{1}{5} $ and much more that are not integers. So we can take any rational number whose fraction doesn’t give an integer value to prove this statement.
Complete step-by-step answer:
In this question, we are supposed to find a number which is rational but not an integer.
So, before proceeding for this, we must know the condition that the rational number is always an integer is not necessary but an integer can be written as a rational number always.
Here, we are said to give an example of the rational number which is not an integer.
But, before that, we all should know what is a rational number.
So, the rational number is the number of the form $ \dfrac{p}{q} $ where $ q\ne 0 $ .
However, an integer is the number that has an integer value and always comes in the total range of numbers from $ -\infty $ to $ \infty $ .
Now, to take an example of any rational number which is not an integer is:
$ \dfrac{3}{4} $
Here, the example considered by us as $ \dfrac{3}{4} $ is not an integer but still a rational number.
Now, to prove that it is not an integer, find the decimal value of the number considered as:
$ \dfrac{3}{4}=0.75 $
So, it gives the value 0.75 and by the definition of integers, it is not an integer value.
But when we go for the definition of rational number, $ \dfrac{3}{4} $ is of form $ \dfrac{p}{q} $ and also its denominator is not zero which states that it is a valid rational number.
Similarly, we can take many numbers which are rational numbers but not integers.
Hence, it is proved that $ \dfrac{3}{4} $ is a rational number but not an integer.
Note: Now, to solve these types of questions, it was not necessary to take this fixed example as $ \dfrac{3}{4} $ to prove that a rational number is not necessarily an integer. So, in mathematics of the numbers, we have a number of rational numbers like $ \dfrac{1}{2},\dfrac{6}{8},\dfrac{1}{5} $ and much more that are not integers. So we can take any rational number whose fraction doesn’t give an integer value to prove this statement.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)