Question

How do you convert $0.49$ ($49$ repeating) as a fraction?

Answer 1

Convert the given repeating decimal into fraction:

Let $\mathrm{x}=0.\overline{49}$ $...\left(\mathrm{i}\right)$

Then $100\mathrm{x}=49.\overline{49}$ $...\left(\mathrm{ii}\right)$ [As the repeating number of digits after decimal are $2$, so multiply both sides by ${10}^2=100$ ]

Now subtract $\left(\mathrm{i}\right)$ from $\left(\mathrm{ii}\right)$, we get;

$100\mathrm{x}-\mathrm{x}=49.\overline{49}-0.\overline{49}$

$\Rightarrow$ $99\mathrm{x}=49$

$\Rightarrow$ $\mathrm{x}=\frac{49}{99}$

Hence, $0.49$ ($49$ repeating) as a fraction is $\frac{49}{99}$.