# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-10/14

Exercises: Try Out - Set 10: Real exam simulation to sharpen your skills and build confidence. - Recurring Decimal Numbers

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## Exercise 14

### Question

export const metadata = {
  title: "Recurring Decimal Numbers",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/27/2025",
};

The recurring decimal number <InlineMath math="1.5454545454..." /> in common fraction form is...


### Choices

- [ ] $$\frac{10}{16}$$
- [ ] $$\frac{11}{17}$$
- [ ] $$\frac{9}{10}$$
- [ ] $$\frac{27}{26}$$
- [x] $$\frac{17}{11}$$

### Answer & Explanation

export const metadata = {
  title: "Recurring Decimal Numbers",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/27/2025",
};

Let <InlineMath math="a = 1.5454545454..." />

Multiply <InlineMath math="a" /> by <InlineMath math="100" />, so:

<MathContainer>
  <BlockMath math="100a = 154.54545454..." />
</MathContainer>

Subtract <InlineMath math="a" /> from <InlineMath math="100a" />, so:

<MathContainer>
  <BlockMath math="100a - a = 154.54545454... - 1.5454545454..." />
  <BlockMath math="99a = 153" />
  <BlockMath math="a = \frac{153}{99} = \frac{17}{11}" />
</MathContainer>

Therefore, the fraction form is <InlineMath math="\frac{17}{11}" />.


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