Question

Express $0.2\overline{54}$ as a fraction in simplest form.

Answer 1

Let $x=\mathrm{0.25454....}$

Now, Multiply 100 on both sides we get

$\Rightarrow$$100x=\mathrm{25.454...}$

Now, substraction x from both side

$\Rightarrow$$100x-x=\mathrm{25.4545.....}-\mathrm{0.2545....}$

We have,

$\Rightarrow$$99x=25.2$

$\Rightarrow$$x=\frac{25.2}{99}$

$\Rightarrow$$x=\frac{252}{990}$