# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-8/1

Exercises: Try Out - Set 8: Real exam simulation to sharpen your skills and build confidence. - Problem 1

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## Exercise 1

### Question

export const metadata = {
  title: "Problem 1",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/25/2025",
};

The common fraction form of the repeating decimal <InlineMath math="0.323323323..." /> is...


### Choices

- [ ] $$\frac{1}{3}$$
- [ ] $$\frac{32}{99}$$
- [ ] $$\frac{23}{99}$$
- [ ] $$\frac{232}{999}$$
- [x] $$\frac{323}{999}$$

### Answer & Explanation

export const metadata = {
  title: "Solution for Problem 1",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/25/2025",
};

Let <InlineMath math="x = 0.323323323..." />. Since there are three repeating digits (<InlineMath math="323" />), multiply both sides by <InlineMath math="1000" />.

<MathContainer>
  <BlockMath math="1000x = 323.323323..." />
</MathContainer>

Next, subtract the original equation <InlineMath math="x = 0.323323..." /> from this equation:

<MathContainer>
  <BlockMath math="\begin{aligned} 1000x &= 323.323323... \\ x &= 0.323323... \\ \hline 999x &= 323 \end{aligned}" />
</MathContainer>

Thus, we get:

<MathContainer>
  <BlockMath math="x = \frac{323}{999}" />
</MathContainer>

So, the common fraction form of the number is <InlineMath math="\frac{323}{999}" />.


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