which fraction represents the decimal 0.8888...?

$\frac{80}{99}$

$\frac{1,111}{1,250}$

$\frac{8}{9}$

$\frac{9}{8}$

Question

which fraction represents the decimal 0.8888...?

$\frac{80}{99}$

$\frac{1,111}{1,250}$

$\frac{8}{9}$

$\frac{9}{8}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Repeating Decimals to Fractions" ], "new_concepts": [], "current_concepts": [ "Repeating Decimals to Fractions", "Geometric Series" ] } ## Express the repeating decimal as an equation Using the *Repeating Decimals to Fractions* knowledge point $$ \begin{aligned} x &= 0.8888\dots \ 10x &= 8.8888\dots \end{aligned} $$ ## Subtract the equations to eliminate the repeating part Using the *Repeating Decimals to Fractions* knowledge point $$ \begin{aligned} 10x - x &= 8.8888\dots - 0.8888\dots \ 9x &= 8 \ x &= \frac{8}{9} \end{aligned} $$

(A) $\frac{80}{99}$

(B) $\frac{1,111}{1,250}$

(C) $\frac{8}{9}$

(D) $\frac{9}{8}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Repeating Decimals to Fractions" ] }

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QUESTION IMAGE

Question

Explanation:

Express the repeating decimal as an equation

Subtract the equations to eliminate the repeating part

Answer: