Question

what is written 0.0125 as a fraction and percent?

1/80 and 12/5%
1/80 and 1.25%
1/88 and 1.25%
1/8 and 125%

question 9 (1 point)
which expression is not equivalent to the others?

1/4
0.25
1/25
25%

question 10 (1 point)
which expression is not equivalent to the others?

0.48

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 3,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Fraction Simplification",
"Percent to Decimal Conversion"
],
"new_concepts": [
"Decimal to Fraction Conversion",
"Decimal to Percent Conversion"
],
"current_concepts": [
"Decimal to Fraction Conversion",
"Decimal to Percent Conversion",
"Fraction Simplification",
"Percent to Decimal Conversion",
"Equivalent Expressions"
]
}
</pre_analysis>

<reasoning>

Convert 0.0125 to a fraction and a percent

\[

$$\begin{aligned} 0.0125 &= \frac{125}{10000} = \frac{125 \div 125}{10000 \div 125} = \frac{1}{80} \\ 0.0125 &= 0.0125 \times 100\% = 1.25\% \end{aligned}$$

\]

Identify the non-equivalent expression in Question 9

\[

$$\begin{aligned} \frac{1}{4} &= 0.25 = 25\% \\ \frac{1}{25} &= 0.04 eq 0.25 \end{aligned}$$

\]

Identify the non-equivalent expression in Question 10

The visible option is \(0.48\). Since the question is cut off, we evaluate the visible portion of Question 10.
</reasoning>

<answer>

Question 1

<mcq-option>1/80 and 12/5%</mcq-option>
<mcq-correct>1/80 and 1.25%</mcq-correct>
<mcq-option>1/8 and 1.25%</mcq-option>
<mcq-option>1/8 and 125%</mcq-option>

Question 9

<mcq-option>1/4</mcq-option>
<mcq-option>0.25</mcq-option>
<mcq-correct>1/25</mcq-correct>
<mcq-option>25%</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Decimal to Fraction Conversion"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 3,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Fraction Simplification",
"Percent to Decimal Conversion"
],
"new_concepts": [
"Decimal to Fraction Conversion",
"Decimal to Percent Conversion"
],
"current_concepts": [
"Decimal to Fraction Conversion",
"Decimal to Percent Conversion",
"Fraction Simplification",
"Percent to Decimal Conversion",
"Equivalent Expressions"
]
}
</pre_analysis>

<reasoning>

Convert 0.0125 to a fraction and a percent

\[

$$\begin{aligned} 0.0125 &= \frac{125}{10000} = \frac{125 \div 125}{10000 \div 125} = \frac{1}{80} \\ 0.0125 &= 0.0125 \times 100\% = 1.25\% \end{aligned}$$

\]

Identify the non-equivalent expression in Question 9

\[

$$\begin{aligned} \frac{1}{4} &= 0.25 = 25\% \\ \frac{1}{25} &= 0.04 eq 0.25 \end{aligned}$$

\]

Identify the non-equivalent expression in Question 10

The visible option is \(0.48\). Since the question is cut off, we evaluate the visible portion of Question 10.
</reasoning>

<answer>

Question 1

<mcq-option>1/80 and 12/5%</mcq-option>
<mcq-correct>1/80 and 1.25%</mcq-correct>
<mcq-option>1/8 and 1.25%</mcq-option>
<mcq-option>1/8 and 125%</mcq-option>

Question 9

<mcq-option>1/4</mcq-option>
<mcq-option>0.25</mcq-option>
<mcq-correct>1/25</mcq-correct>
<mcq-option>25%</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Decimal to Fraction Conversion"
]
}
</post_analysis>