the repeating decimal, $0.\overline{27}$, is converted to the fraction $0.\overline{27} = \frac{3}{x}$.

what is the value of $x$ in the fraction?

Question

the repeating decimal, $0.\overline{27}$, is converted to the fraction $0.\overline{27} = \frac{3}{x}$.

what is the value of $x$ in the fraction?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Repeating Decimal Conversion" ], "new_concepts": [], "current_concepts": [ "Repeating Decimal Conversion", "Algebraic Substitution" ] } ## Convert the repeating decimal to a fraction $$ 0.\overline{27} = \frac{27}{99} $$ ## Simplify the fraction $$ \frac{27}{99} = \frac{27 \div 9}{99 \div 9} = \frac{3}{11} $$ ## Solve for x $$ \begin{aligned} \frac{3}{11} &= \frac{3}{x} \ x &= 11 \end{aligned} $$ The repeating decimal, $0.\overline{27}$, is converted to the fraction $0.\overline{27} = \frac{3}{x}$. What is the value of $x$ in the fraction? 11 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Repeating Decimal Conversion" ] }

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QUESTION IMAGE

Question

Explanation:

Convert the repeating decimal to a fraction

Simplify the fraction

Solve for x

Answer: