Question

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

Answer 1

Answer:

$\frac{11}{25}$

Step-by-step explanation:

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

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

$= \frac{99}{100} \cdot\frac{4}{9}$

We can simplify the product :

$=\frac{396}{900} = \frac{132}{300} = \frac{44}{100} = \frac{11}{25}$

The final answer is $\frac{11}{25}$

-Chetan K