# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-9/16

Exercises: Try Out - Set 9: Real exam simulation to sharpen your skills and build confidence. - Question 16

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## Exercise 16

### Question

export const metadata = {
    title: "Question 16",
    authors: [{ name: "Nabil Akbarazzima Fatih" }],
    date: "12/26/2025",
};

The fractional form of the repeating decimal <InlineMath math="3.15931593..." /> is?


### Choices

- [ ] $$\frac{1170}{37}$$
- [x] $$\frac{3510}{1111}$$
- [ ] $$\frac{1177}{111}$$
- [ ] $$\frac{1170}{999}$$
- [ ] $$\frac{1177}{999}$$

### Answer & Explanation

export const metadata = {
  title: "Solution 16",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/26/2025",
};

Let <InlineMath math="x = 3.15931593..." />.

Since there are <InlineMath math="4" /> repeating digits (which are <InlineMath math="1593" />), we multiply <InlineMath math="x" /> by <InlineMath math="10000" />:

<MathContainer>
  <BlockMath math="10000x = 31593.15931593..." />
</MathContainer>

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

<MathContainer>
  <BlockMath math="\begin{aligned} 10000x &= 31593.1593... \\ x &= \phantom{3159}3.1593... \\ \hline 9999x &= 31590 \end{aligned}" />
</MathContainer>

Thus, we obtain:

<MathContainer>
  <BlockMath math="x = \frac{31590}{9999}" />
</MathContainer>

We simplify the fraction by dividing both the numerator and the denominator by <InlineMath math="9" />:

<MathContainer>
  <BlockMath math="x = \frac{31590 \div 9}{9999 \div 9} = \frac{3510}{1111}" />
</MathContainer>


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