Question
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2. Which decimal is equivalent to \( \frac{6}{11} \) ? A. \( 0.18 \overline{3} \) B. \( 0.1 \overline{83} \) C. \( 0.5 \overline{4} \) D. \( 0 . \overline{54} \)

Ask by Washington Blake. in the United States
Jan 24,2025

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Answer

La fracción \( \frac{6}{11} \) es igual al decimal \( 0.\overline{54} \).

Solution

La fracción \( \frac{6}{11} \) es equivalente al decimal periódico \( 0.\overline{54} \). **Por lo tanto, la respuesta correcta es la opción D.** **Explicación:** Al dividir 6 entre 11: \[ 6 \div 11 = 0.545454\ldots = 0.\overline{54} \] Esto muestra que el decimal se repite indefinidamente con "54".

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Extra Insights

To convert the fraction \( \frac{6}{11} \) into a decimal, you can perform long division or recognize that it has a repeating pattern. Dividing 6 by 11 gives us \( 0.545454... \), which can be written as \( 0.\overline{54} \). So, the correct answer is D. If you're ever confused about identifying repeating decimals, remember that the notation \( 0.\overline{ab} \) signifies that the digits \( ab \) repeat indefinitely. In this case, for \( 0.\overline{54} \), both the 5 and 4 will continue on forever, creating that charming cycling effect that decimal lovers adore! A great way to practice converting fractions to decimals is to explore online tools or apps. These resources often allow you to input various fractions, and they'll display the decimal equivalents. Just remember to look out for those repeating decimals, as they can be tricky!

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