
How do you convert to a fraction?
Answer
481.2k+ views
Hint: In this problem we need to convert the given decimal into the fraction. Generally, the conversion of the decimals into fractions depends on whether the digits in the decimal are being repeated or not. In the problem, they have mentioned that the digits are repeating. So, we will first assume the given decimal is equal to a variable let’s say . Now we will observe how many digits are repeated in the given decimal. We need to multiply with where is the number of repeated digits. Now we will subtract both the values and simplify them to get the result.
Complete step by step solution:
Given decimal .
Let
Given that is being repeated. In we have digits. So, we will multiple with on both sides of the above equation, then we will get
We know that , then we will have
Given that is being repeated, so we can write
Subtracting the value of from the above equation, then we will get
Dividing the above equation with on both sides, then we will get
We can write and , then we will get
Cancelling the in numerator and denominator, then we will have
Hence the fraction of is .
Note:
In the problem, they mentioned that the digits are repeated. So, we have followed the above method. If they have not mentioned that the digits are not repeated, then it can be easier to convert the decimal into a fraction. We have two digits after the decimal so we will divide the given number with and remove the decimal. Then we will get .
Complete step by step solution:
Given decimal
Let
Given that
We know that
Given that
Subtracting the value of
Dividing the above equation with
We can write
Cancelling the
Hence the fraction of
Note:
In the problem, they mentioned that the digits are repeated. So, we have followed the above method. If they have not mentioned that the digits are not repeated, then it can be easier to convert the decimal into a fraction. We have two digits after the decimal so we will divide the given number with
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