Answer:
[tex]\bold{x = \dfrac{8}{9}}[/tex]
Step-by-step explanation:
We have to rewrite the below as simplified fraction.
[tex]\large{0.\overline{8} = {?}}[/tex]
Solution:
Let [tex]x =0.\overline 8[/tex] which means [tex]x =0.888888.......[/tex]
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 [tex]x[/tex] as:
[tex]x =0.8\overline8[/tex] ......(1)
Now, let us multiply the above with 10.
[tex]10x = 0.8\overline 8 \times 10\\\Rightarrow 10 x= 8.\overline8[/tex] ....... (2)
Now, let us subtract (1) from (2):
[tex]10x-x=8.\overline8 - 0.\overline8\\\Rightarrow 9x = 8\\\Rightarrow \bold{x = \dfrac{8}{9}}[/tex]
So, in simplified fractions:
[tex]\large{0.\overline{8} = \bold{\dfrac{8}{9}}}[/tex]
