Question

How do you change $0.244444444$ into fraction?

Answer 1

Hint: We know that fraction represents equal parts of a whole or a collection. When we divide a whole into equal parts, each part is a fraction of the whole. We will assume as x. Then we will compute 10x. Subtracting 10x and x, we will be able to get the value of x. It will give us the fraction form.

Complete step-by-step answer:
Now, the given question is $0.244444444$. This expression is in the decimal form. Actually the decimal is a fraction written in a special form. It means we can easily express the fraction in the decimal form. Here we have to calculate the fraction form of the given $0.244444444$.
Now let $x=0.244444444$ $..........\left( 1 \right)$
And now multiply the above expression with $10$, then we get
$\Rightarrow 10x=2.44444444$ $.....\left( 2 \right)$
Now subtracting the equation (1) from equation (2), then we get
$\begin{align}
  & \Rightarrow 10x-x=2.44444444-0.244444444 \\
 & \Rightarrow 9x=2.2 \\
\end{align}$
Now write the above $2.2$ in a mixed fraction we get,
$\Rightarrow 9x=2\dfrac{2}{10}$
Now by more simplifying we get
$\begin{align}
  & \Rightarrow x=\dfrac{2}{9}+\dfrac{2}{90} \\
 & \Rightarrow x=\dfrac{20+2}{90} \\
 & \Rightarrow x=\dfrac{22}{90} \\
\end{align}$
Now by more simplifying we get$\Rightarrow x=\dfrac{11}{45}$
Hence we get the fraction form of the given expression $0.244444444$ which is as $\dfrac{11}{45}$ .

Note: We can also solve the above expression by another method.
As we know $0.24$ is less than $1$ so the continued fraction starts with $0+\dfrac{1}{0.2\overset{.}{\mathop{4}}\,}$
Now calculate $\dfrac{1}{0.2\overset{.}{\mathop{4}}\,}$ which is equal to $4.\overset{.}{\mathop{0}}\,\overset{.}{\mathop{9}}\,$
So our continued fraction looks like$0+\dfrac{1}{4+\dfrac{1}{...}}$
Now subtract $4$ from the above fraction and then calculate $\dfrac{1}{0.\overset{.}{\mathop{0}}\,\overset{.}{\mathop{9}}\,}=11$
Now we get our fraction terminates here so we can write
$\Rightarrow 0+\dfrac{1}{4+\dfrac{1}{11}}$
Now solving the above fraction we get
$\Rightarrow \dfrac{1}{\dfrac{44+1}{11}}=\dfrac{1}{\dfrac{45}{11}}=\dfrac{11}{45}$
Here we get the same answer as we solved above. The fraction form of the given decimal expression $0.244444444$ is $\dfrac{11}{45}$.