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# Convert the recurring decimal $0.\overline {35}$ to fraction.

Last updated date: 19th Jul 2024
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Hint- In this problem statement we have to convert the given recurring decimal to a fraction. First let’s talk about a recurring decimal. A recurring decimal also known as a repeating decimal basically refers to a number whose digits repeats till infinite times after a regular interval of time. So in order to convert it into fraction simply consider it equal to a variable and proceed, this will help to reach the answer.

Now we have to convert recurring decimal $0.\overline {35}$ into fraction.
Let x= $0.\overline {35}$…………. (1)
100x=$35.\overline {35}$…………… (2)
Now we can write $35.\overline {35} = 35 + 0.\overline {35}$
$100x = 35 + 0.\overline {35}$
$\Rightarrow 100x = 35 + x$
$\begin{gathered} 99x = 35 \\ \Rightarrow x = \dfrac{{35}}{{99}} \\ \end{gathered}$
Hence the fraction conversion of $0.\overline {35}$ is $\dfrac{{35}}{{99}}$.