which simplified fraction is equal to (0.1\bar{7})?

* (\frac{9}{17})
* (\frac{8}{45})
* (\frac{17}{9})
* (\frac{16}{90})

Question

which simplified fraction is equal to (0.1\bar{7})?

* (\frac{9}{17})
* (\frac{8}{45})
* (\frac{17}{9})
* (\frac{16}{90})

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Repeating Decimals" ], "new_concepts": [ "Repeating Decimal Conversion" ], "current_concepts": [ "Repeating Decimals", "Repeating Decimal Conversion" ] } ## Set up the algebraic equation $$ \begin{aligned} x &= 0.1\overline{7} \ 10x &= 1.7\overline{7} \ 100x &= 17.7\overline{7} \end{aligned} $$ ## Subtract the equations to eliminate the repeating part $$ \begin{aligned} 100x - 10x &= 17.7\overline{7} - 1.7\overline{7} \ 90x &= 16 \end{aligned} $$ ## Solve for x and simplify the fraction $$ \begin{aligned} x &= \frac{16}{90} \ x &= \frac{8}{45} \end{aligned} $$

(A) $\frac{9}{17}$

(B) $\frac{8}{45}$

(C) $\frac{17}{9}$

(D) $\frac{16}{90}$

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

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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: