Question

Rewrite as a simplified fraction.

Answer 1

Answer:

$\bold{x = \dfrac{8}{9}}$

Step-by-step explanation:

We have to rewrite the below as simplified fraction.

$\large{0.\overline{8} = {?}}$

Solution:

Let $x =0.\overline 8$ which means $x =0.888888.......$

Here a bar over 8 means that there the given decimal value is non terminating and there are a large numbers of 8 present after the decimal.

To solve the given non terminating decimal as fractions, we will have to eliminate the bar term from the given value.

So, we can rewrite $x$ as:

$x =0.8\overline8$ ......(1)

Now, let us multiply the above with 10.

$10x = 0.8\overline 8 \times 10\\\Rightarrow 10 x= 8.\overline8$ ....... (2)

Now, let us subtract (1) from (2):

$10x-x=8.\overline8 - 0.\overline8\\\Rightarrow 9x = 8\\\Rightarrow \bold{x = \dfrac{8}{9}}$

So, in simplified fractions:

$\large{0.\overline{8} = \bold{\dfrac{8}{9}}}$