Question

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

Hint- In this problem statement we have to convert the given recurring decimal to a fraction. First letâ€™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= $0.\overline {35}$â€¦â€¦â€¦â€¦. (1)
Multiplying with 100 both the side of equation (1) we get,
100x=$35.\overline {35}$â€¦â€¦â€¦â€¦â€¦ (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 â€“ 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.