Answer
385.5k+ views
Hint: In this question, we need to convert $0.23\bar 4$ (with $4$ repeating) into fraction. Here, we will consider $0.23\bar 4$ as x. So, to bring the repeating entity immediately after the decimal point, we multiply and divide the given decimal $0.23\bar 4$ by $100$. Then, as there is only $1$ digit being repeated. So, we multiply and divide the decimal by $10$.
Complete step-by-step solution:
In this question, we need to convert $0.23\bar 4$ to a fraction.
Let x be that fraction.
Here, consider the given value as $x = 0.23\bar 4$.
Now, let us multiply and divide $0.23\bar 4$ by $100$, we have,
$x = 0.23\bar 4 \times \dfrac{{100}}{{100}}$
Then, $100x = 0.23\bar 4 \times 100$
$ \Rightarrow 100x = 23.\bar 4$
Hence, $100x = 23.4444....$
Let us consider this as the equation $\left( 1 \right)$.
Now, let us multiply and divide $23.\bar 4$ by $10$, we have,
$100x = 23.\bar 4 \times \left( {\dfrac{{10}}{{10}}} \right)$
Then, $1000x = 23.\bar 4 \times 10$
$ \Rightarrow 1000x = 234.\bar 4$
Hence, $1000x = 234.\bar 4$
Let us consider this as equation \[\left( 2 \right)\].
Now, we will subtract equation $\left( 1 \right)$ from equation \[\left( 2 \right)\].
Therefore, we have,
$1000x - 100x = \left( {234.\bar 4 - 23.\bar 4} \right)$
Hence, $900x = \left( {234.4444.... - 23.4444.....} \right)$
$ \Rightarrow 900x = 211$
\[ \Rightarrow x = \dfrac{{211}}{{900}}\]
Therefore, \[x = \dfrac{{211}}{{900}}\]
Hence, the converted value of $0.23\bar 4$ to a fraction is \[\left( {\dfrac{{211}}{{900}}} \right)\].
Note: In this question it is important to note that, here we have multiplied and divided $0.23\bar 4$ firstly by $100$ and then by $10$ respectively, then subtracted both the equations to determine the value of x as in this question we have a repetition of a repetition of $4$ in $0.23\bar 4$. The scenario may be different in each question depending on the situation as the decimal may have more number of digits as its repeating entity.
Complete step-by-step solution:
In this question, we need to convert $0.23\bar 4$ to a fraction.
Let x be that fraction.
Here, consider the given value as $x = 0.23\bar 4$.
Now, let us multiply and divide $0.23\bar 4$ by $100$, we have,
$x = 0.23\bar 4 \times \dfrac{{100}}{{100}}$
Then, $100x = 0.23\bar 4 \times 100$
$ \Rightarrow 100x = 23.\bar 4$
Hence, $100x = 23.4444....$
Let us consider this as the equation $\left( 1 \right)$.
Now, let us multiply and divide $23.\bar 4$ by $10$, we have,
$100x = 23.\bar 4 \times \left( {\dfrac{{10}}{{10}}} \right)$
Then, $1000x = 23.\bar 4 \times 10$
$ \Rightarrow 1000x = 234.\bar 4$
Hence, $1000x = 234.\bar 4$
Let us consider this as equation \[\left( 2 \right)\].
Now, we will subtract equation $\left( 1 \right)$ from equation \[\left( 2 \right)\].
Therefore, we have,
$1000x - 100x = \left( {234.\bar 4 - 23.\bar 4} \right)$
Hence, $900x = \left( {234.4444.... - 23.4444.....} \right)$
$ \Rightarrow 900x = 211$
\[ \Rightarrow x = \dfrac{{211}}{{900}}\]
Therefore, \[x = \dfrac{{211}}{{900}}\]
Hence, the converted value of $0.23\bar 4$ to a fraction is \[\left( {\dfrac{{211}}{{900}}} \right)\].
Note: In this question it is important to note that, here we have multiplied and divided $0.23\bar 4$ firstly by $100$ and then by $10$ respectively, then subtracted both the equations to determine the value of x as in this question we have a repetition of a repetition of $4$ in $0.23\bar 4$. The scenario may be different in each question depending on the situation as the decimal may have more number of digits as its repeating entity.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 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)
Give 10 examples for herbs , shrubs , climbers , creepers
![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)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english 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)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)