Question

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

Answer 1

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.