Question

Rewrite as a simplified fraction.

\large{0.\overline{8} = {?}}0.
8
=?0, point, start overline, 8, end overline, equals, question mark

Answer 1

`\bold{x = (8)/(9)}`

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 * 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 = (8)/(9)}`

So, in simplified fractions:

`\large{0.\overline{8} = \bold{(8)/(9)}}`