# Nakafa Framework: LLM

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

Exercises: Try Out - Set 10: Simulasi ujian nyata untuk mengasah kemampuan dan kepercayaan diri. - Bilangan Desimal Berulang

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## Exercise 14

### Question

export const metadata = {
  title: "Bilangan Desimal Berulang",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/27/2025",
};

Bilangan desimal berulang <InlineMath math="1,5454545454.." /> bentuk pecahan biasanya adalah...


### Choices

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

### Answer & Explanation

export const metadata = {
  title: "Bilangan Desimal Berulang",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/27/2025",
};

Misalkan <InlineMath math="a = 1,5454545454..." />

Kalikan <InlineMath math="a" /> dengan <InlineMath math="100" /> sehingga:

<MathContainer>
  <BlockMath math="100a = 154,54545454..." />
</MathContainer>

Kurangkan <InlineMath math="100a" /> dengan <InlineMath math="a" /> sehingga:

<MathContainer>
  <BlockMath math="100a - a = 154,54545454... - 1,5454545454..." />
  <BlockMath math="99a = 153" />
  <BlockMath math="a = \frac{153}{99} = \frac{17}{11}" />
</MathContainer>

Jadi, bentuk pecahan biasanya adalah <InlineMath math="\frac{17}{11}" />.


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