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

Answer

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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.

Complete step-by-step answer:

Now we have to convert recurring decimal $0.\overline {35} $ into fraction.

Let x= $0.\overline {35} $…………. (1)

Multiplying with 100 both the side of equation (1) we get,

100x=$35.\overline {35} $…………… (2)

Now we can write $35.\overline {35} = 35 + 0.\overline {35} $

So equation (2) gets changed to

$100x = 35 + 0.\overline {35} $

Now using equation (1) we get,

$ \Rightarrow 100x = 35 + x$

On simplifying further we get,

$\begin{gathered}

99x = 35 \\

\Rightarrow x = \dfrac{{35}}{{99}} \\

\end{gathered} $

Hence the fraction conversion of $0.\overline {35} $ is $\dfrac{{35}}{{99}}$.

Note – Whenever we face such types of problems the key point is to simplify the fraction conversion for the given recurring number as a variable, then proper simplification of this equation will help you get on the right track to solve for that variable, this will give the fraction conversion for the recurring number.

Complete step-by-step answer:

Now we have to convert recurring decimal $0.\overline {35} $ into fraction.

Let x= $0.\overline {35} $…………. (1)

Multiplying with 100 both the side of equation (1) we get,

100x=$35.\overline {35} $…………… (2)

Now we can write $35.\overline {35} = 35 + 0.\overline {35} $

So equation (2) gets changed to

$100x = 35 + 0.\overline {35} $

Now using equation (1) we get,

$ \Rightarrow 100x = 35 + x$

On simplifying further we get,

$\begin{gathered}

99x = 35 \\

\Rightarrow x = \dfrac{{35}}{{99}} \\

\end{gathered} $

Hence the fraction conversion of $0.\overline {35} $ is $\dfrac{{35}}{{99}}$.

Note – Whenever we face such types of problems the key point is to simplify the fraction conversion for the given recurring number as a variable, then proper simplification of this equation will help you get on the right track to solve for that variable, this will give the fraction conversion for the recurring number.

Last updated date: 27th Sep 2023

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