Find five rational numbers between 1 and 2.
Last updated date: 15th Mar 2023
•
Total views: 212.9k
•
Views today: 2.92k
Answer
212.9k+ views
Hint- consider any five numbers between 1 and 2 and convert them into lowest form fraction.
As we know rational numbers are those which are written in the form of $\dfrac{p}{q}$, where $q \ne 0 $and $\dfrac{p}{q}$ is written in lowest form, such that $p$ and $q$ have not no common factors except 1.
For example $\dfrac{2}{3}$ as this fraction is written in lowest form and does not have any common factors except 1, so this is a rational number.
Now we have to find out the rational numbers between 1 and 2
I.e. greater than 1 and less than 2.
So consider five numbers between 1 and 2 which is $\left\{ {1.1,1.2,1.3,1.4,1.5} \right\}$
Now, convert these numbers into fraction
$1.1 = \dfrac{{11}}{{10}},{\text{ }}1.2 = \dfrac{{12}}{{10}},{\text{ }}1.3 = \dfrac{{13}}{{10}},{\text{ }}1.4 = \dfrac{{14}}{{10}},{\text{ }}1.5 = \dfrac{{15}}{{10}},$
Now, convert these fraction into lowest form such that these fraction have not any common factors
$
\Rightarrow 1.1 = \dfrac{{11}}{{10}} \\
\Rightarrow 1.2 = \dfrac{{12}}{{10}} = \dfrac{6}{5} \\
\Rightarrow 1.3 = \dfrac{{13}}{{10}} \\
\Rightarrow 1.4 = \dfrac{{14}}{{10}} = \dfrac{7}{5} \\
\Rightarrow 1.5 = \dfrac{{15}}{{10}} = \dfrac{3}{2} \\
$
So, $\left\{ {\dfrac{{11}}{{10}},\dfrac{6}{5},\dfrac{{13}}{{10}},\dfrac{7}{5},\dfrac{3}{2}} \right\}$ are the required five rational numbers between 1 and 2.
Note: - In such types of problems the key concept we have to remember is that always remember the condition of rational number which is stated above, then assume any five numbers between 1 and 2, then convert them into fraction then convert them into lowest form fraction such that the fractions have not any common factors, then we will get the required answer.
As we know rational numbers are those which are written in the form of $\dfrac{p}{q}$, where $q \ne 0 $and $\dfrac{p}{q}$ is written in lowest form, such that $p$ and $q$ have not no common factors except 1.
For example $\dfrac{2}{3}$ as this fraction is written in lowest form and does not have any common factors except 1, so this is a rational number.
Now we have to find out the rational numbers between 1 and 2
I.e. greater than 1 and less than 2.
So consider five numbers between 1 and 2 which is $\left\{ {1.1,1.2,1.3,1.4,1.5} \right\}$
Now, convert these numbers into fraction
$1.1 = \dfrac{{11}}{{10}},{\text{ }}1.2 = \dfrac{{12}}{{10}},{\text{ }}1.3 = \dfrac{{13}}{{10}},{\text{ }}1.4 = \dfrac{{14}}{{10}},{\text{ }}1.5 = \dfrac{{15}}{{10}},$
Now, convert these fraction into lowest form such that these fraction have not any common factors
$
\Rightarrow 1.1 = \dfrac{{11}}{{10}} \\
\Rightarrow 1.2 = \dfrac{{12}}{{10}} = \dfrac{6}{5} \\
\Rightarrow 1.3 = \dfrac{{13}}{{10}} \\
\Rightarrow 1.4 = \dfrac{{14}}{{10}} = \dfrac{7}{5} \\
\Rightarrow 1.5 = \dfrac{{15}}{{10}} = \dfrac{3}{2} \\
$
So, $\left\{ {\dfrac{{11}}{{10}},\dfrac{6}{5},\dfrac{{13}}{{10}},\dfrac{7}{5},\dfrac{3}{2}} \right\}$ are the required five rational numbers between 1 and 2.
Note: - In such types of problems the key concept we have to remember is that always remember the condition of rational number which is stated above, then assume any five numbers between 1 and 2, then convert them into fraction then convert them into lowest form fraction such that the fractions have not any common factors, then we will get the required answer.
Recently Updated Pages
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

A Short Paragraph on our Country India
