Answer
398.4k+ views
Hint: In this problem, we have to find the fraction for the given decimal. We can first assume x to the given decimal. We can then multiply the both to 10 and 100, we will get two equations. We can then subtract the both equations to get the value of x, that is the exact fraction of the given decimal number.
Complete step by step answer:
We know that the given decimal number to be converted into its fraction is 0.87, where 7 is repeated, so we can write as 0.87777….
We can assume the decimal number to x, we get
\[\Rightarrow x=0.8777...\] ….. (1)
Now we can multiply the number 10 on both sides were in right-hand side the decimal point moves one point to the right, we get
\[\Rightarrow 10x=8.777...\] ….. (2)
Now we can multiply 100 on both side of equation (1), we get
\[\Rightarrow 100x=87.777...\] …. (3)
We can now subtract the equation (2) and (3), we get
\[\Rightarrow 90x=79.00\]
We can now divide the number 90 on both the sides, we get
\[\Rightarrow x=\dfrac{79}{90}\]
Therefore, the fractional form of the decimal 0.87 (7 being repeated) is \[\dfrac{79}{90}\].
Note: Students make mistakes while reading the question properly, here ‘7 is being repeated’ is an important point to be noted. We should also know that if we multiply a decimal number by 10 and 100, we should move the decimal point 1 and 2 points to the right respectively.
Complete step by step answer:
We know that the given decimal number to be converted into its fraction is 0.87, where 7 is repeated, so we can write as 0.87777….
We can assume the decimal number to x, we get
\[\Rightarrow x=0.8777...\] ….. (1)
Now we can multiply the number 10 on both sides were in right-hand side the decimal point moves one point to the right, we get
\[\Rightarrow 10x=8.777...\] ….. (2)
Now we can multiply 100 on both side of equation (1), we get
\[\Rightarrow 100x=87.777...\] …. (3)
We can now subtract the equation (2) and (3), we get
\[\Rightarrow 90x=79.00\]
We can now divide the number 90 on both the sides, we get
\[\Rightarrow x=\dfrac{79}{90}\]
Therefore, the fractional form of the decimal 0.87 (7 being repeated) is \[\dfrac{79}{90}\].
Note: Students make mistakes while reading the question properly, here ‘7 is being repeated’ is an important point to be noted. We should also know that if we multiply a decimal number by 10 and 100, we should move the decimal point 1 and 2 points to the right respectively.
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)