Respuesta :
Answer: The decimal 0.88888.... represented by the fraction [tex]\dfrac{8}{9}[/tex]
Step-by-step explanation:
Since we have given that
0.888888....
So, Let x = 0.88888....=[tex]0.\bar{8}[/tex] -----(1)
Now, multiply by 10 on both sides, we get that
[tex]10x=8.8888.....=8.\bar{8}----------(2)[/tex]
Now, Subtracting (1) from (2), we get that
[tex]10x-x=8.\bar{8}-0.\bar{8}\\\\9x=8\\\\x=\dfrac{8}{9}[/tex]
Hence, the decimal 0.88888.... represented by the fraction [tex]\dfrac{8}{9}[/tex]
