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1. Which decimal is equivalent to \( \frac{11}{15} \) ? (A) \( 0 . \overline{733} \) (a) 0.73 (c) \( 0.7 \overline{3} \)

Ask by John Dawson. in the United States
Feb 25,2025

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Tutor-Verified Answer

Answer

The decimal equivalent of \( \frac{11}{15} \) is 0.7 overline{3}.

Solution

To convert 11/15 to a decimal, perform the division:  • Divide 11.000 by 15.  • 15 goes into 11 zero times. Write 0.  • Bring down a 0 to make 110. 15 goes into 110 seven times (15 × 7 = 105) with a remainder of 5.  • Bring down another 0 to make 50. 15 goes into 50 three times (15 × 3 = 45) with a remainder of 5.  • The remainder is still 5, so each time you bring down a 0, you'll get 3, repeating indefinitely. Thus, 11/15 = 0.7 followed by repeating 3’s, which is written as 0.7overline{3}. Comparing with the given options, the correct answer is: (c) 0.7overline{3}

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The Deep Dive

To find the decimal equivalent of \( \frac{11}{15} \), you can perform long division. Dividing 11 by 15 gives 0.7333... where the 3 repeats indefinitely. Therefore, the equivalent decimal is \( 0.7 \overline{3} \), making (c) the correct answer. Interestingly, fractions that lead to repeating decimals arise from denominators that aren't powers of 10. The 15 in \( \frac{11}{15} \) leads to a decimal representation that loops, so you can impress your friends by saying, "Look! I can find the pattern in my decimal!"

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