The recurring decimal representation 1.272727... is equivalent to
- A13/11
- B14/11Correct
- C127/99
- D137/99
Explanation
To convert a recurring decimal to a fraction, follow these steps:
-
Let x equal the given recurring decimal: x = 1.272727... (Equation 1)
-
Identify the repeating part. Here, '27' is the repeating block. Since there are two digits in the repeating block, multiply Equation 1 by 100: 100x = 127.272727... (Equation 2)
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Subtract Equation 1 from Equation 2: 100x - x = 127.272727... - 1.272727... 99x = 126
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Solve for x: x = 126 / 99
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Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 9: x = (126 ÷ 9) / (99 ÷ 9) x = 14 / 11
Therefore, 1.272727... is equivalent to 14/11.
Analyzing the options: A) 13/11 = 1.181818... (Incorrect) B) 14/11 = 1.272727... (Correct) C) 127/99 = 1.282828... (Incorrect) D) 137/99 = 1.383838... (Incorrect)
The final answer is B.
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