which simplified fraction is equal to (0.5\bar{3})?

* (\frac{24}{46})
* (\frac{8}{15})
* (\frac{42}{90})
* (\frac{5}{9})

Question

which simplified fraction is equal to (0.5\bar{3})?

* (\frac{24}{46})
* (\frac{8}{15})
* (\frac{42}{90})
* (\frac{5}{9})

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Repeating Decimal Conversion" ], "new_concepts": [], "current_concepts": [ "Repeating Decimal Conversion", "Repeating Decimals" ] } ## Set up the algebraic equation $$ \begin{aligned} x &= 0.5\overline{3} \ 10x &= 5.\overline{3} \ 100x &= 53.\overline{3} \end{aligned} $$ ## Subtract the equations to eliminate the repeating part $$ \begin{aligned} 100x - 10x &= 53.\overline{3} - 5.\overline{3} \ 90x &= 48 \end{aligned} $$ ## Solve for x and simplify the fraction $$ \begin{aligned} x &= \frac{48}{90} \ x &= \frac{48 \div 6}{90 \div 6} = \frac{8}{15} \end{aligned} $$

(A) $\frac{24}{46}$

(B) $\frac{8}{15}$

(C) $\frac{42}{90}$

(D) $\frac{5}{9}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Repeating Decimal Conversion" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the algebraic equation

Subtract the equations to eliminate the repeating part

Solve for x and simplify the fraction

Answer: