which fraction represents the decimal 0.8888...?\n$\frac{80}{99}$\n$\frac{1,111}{1,250}$\n$\frac{8}{9}$\n$\fr…

which fraction represents the decimal 0.8888...?\n$\frac{80}{99}$\n$\frac{1,111}{1,250}$\n$\frac{8}{9}$\n$\frac{9}{8}$

which fraction represents the decimal 0.8888...?\n$\frac{80}{99}$\n$\frac{1,111}{1,250}$\n$\frac{8}{9}$\n$\frac{9}{8}$

Answer

Answer:

C. $\frac{8}{9}$

Explanation:

Step1: Let $x = 0.888\cdots$

$x=0.8 + 0.08+0.008+\cdots$

Step2: Recognize as geometric series

This is an infinite geometric - series with first term $a = 0.8$ and common ratio $r=0.1$.

Step3: Use geometric - series formula

The sum of an infinite geometric series is $S=\frac{a}{1 - r}$. Substitute $a = 0.8=\frac{8}{10}$ and $r = 0.1=\frac{1}{10}$ into the formula: $S=\frac{\frac{8}{10}}{1-\frac{1}{10}}$.

Step4: Simplify the expression

$S=\frac{\frac{8}{10}}{\frac{9}{10}}=\frac{8}{9}$.