Question

Write $\frac{99}{100}\cdot(0.\overline{4})$ as a fully simplified fraction.
Please help

Answer 1

`(11)/(25)`

Explanation:

`$(99)/(100)\cdot(0.\overline{4})$`

Let's rewrite
`\overline{0.4}` as a fraction:

Let x = 0.4444444.....

10x = 4.444444....

9x = 4.44444.... - 0.44444....

9x = 4

x = 4/9

Now we can multiply the two fractions regularly

`= (99)/(100) \cdot(4)/(9)`

We can simplify the product :

`=(396)/(900) = (132)/(300) = (44)/(100) = (11)/(25)`

The final answer is
`(11)/(25)`

-Chetan K