Question

write the decimal as an improper fraction.
2.18

\\(\frac{109}{500}\\)
\\(\frac{111}{500}\\)
\\(\frac{109}{50}\\)
\\(\frac{111}{50}\\)

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Simplifying Fractions",
"Place Value"
],
"new_concepts": [
"Converting Decimals to Fractions"
],
"current_concepts": [
"Place Value",
"Simplifying Fractions",
"Converting Decimals to Fractions"
]
}
</pre_analysis>

<reasoning>

Convert the decimal to a fraction

\[
2.18 = \frac{218}{100}
\]

Simplify the fraction by dividing by the greatest common divisor

\[
\frac{218 \div 2}{100 \div 2} = \frac{109}{50}
\]
</reasoning>

<answer>
<mcq-option>(A) \(\frac{109}{500}\)</mcq-option>
<mcq-option>(B) \(\frac{111}{500}\)</mcq-option>
<mcq-correct>(C) \(\frac{109}{50}\)</mcq-correct>
<mcq-option>(D) \(\frac{111}{50}\)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Converting Decimals to Fractions"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
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"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Simplifying Fractions",
"Place Value"
],
"new_concepts": [
"Converting Decimals to Fractions"
],
"current_concepts": [
"Place Value",
"Simplifying Fractions",
"Converting Decimals to Fractions"
]
}
</pre_analysis>

<reasoning>

Convert the decimal to a fraction

\[
2.18 = \frac{218}{100}
\]

Simplify the fraction by dividing by the greatest common divisor

\[
\frac{218 \div 2}{100 \div 2} = \frac{109}{50}
\]
</reasoning>

<answer>
<mcq-option>(A) \(\frac{109}{500}\)</mcq-option>
<mcq-option>(B) \(\frac{111}{500}\)</mcq-option>
<mcq-correct>(C) \(\frac{109}{50}\)</mcq-correct>
<mcq-option>(D) \(\frac{111}{50}\)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Converting Decimals to Fractions"
]
}
</post_analysis>