Question

How do you convert $0.916$ $\left( 6\,repeating \right)$ to a fraction?

Answer 1

Hint: From the above question we have to convert the $0.916$ $\left( 6 \,repeating \right)$ into a fraction. Here $0.916$$\left( 6\,repeating \right)$ can be written as $0.91\bar{6}$, to convert into a fraction first we have to assume a variable let “x” is the given decimal then we have to multiply both sides with $100$ and $1000$, after that we have to subtract the $1000x-100x$, from this we will get the variable “x” in a fraction form.

Complete step by step solution:
From the above question we have to convert given decimal into fraction, the given decimal is,
$\Rightarrow 0.916\left( 6 \,repeating \right)$
As we know that it can be written as
$\Rightarrow 0.916\left( 6 \,repeating \right)=0.91666666\cdots =0.91\bar{6}$
Now we have to assume that the variable “x” is equal to the given decimal that is,
$\Rightarrow x=0.91\bar{6}$
First, we have to multiply both sides with $100$,
By multiplying we will get,
$\Rightarrow 100x=91.\bar{6}$
Now we have to multiply both sides with $1000$,
By multiplying we will get,
$\Rightarrow 1000x=916.\bar{6}$
Now we have to subtract the $100x$ from $1000x$, that is,
$\Rightarrow 1000x-100x$
By doing subtraction we will get,
$\Rightarrow 1000x-100x=916.\bar{6}-91.\bar{6}$
By further simplification we will get,
$\Rightarrow 900x=825.0$
Now we have shift the $900$ from left hand side to the right-hand side,
By shifting $900$ from left hand side to the right-hand side, we will get,
$\Rightarrow x=\dfrac{825}{900}$
By further simplification we will get,
$\Rightarrow x=\dfrac{11}{12}$
Therefore, the conversion of $0.91\bar{6}$ into a fraction is $\dfrac{11}{12}$.

Note: Students should know the conversion of decimals into the fraction, if in the question there is no $\left( 6\,repeating \right)$ term means students can write directly $0.916$ as $\dfrac{916}{1000}$ then we can do further simplification to get simplified fraction.