Which decimal is a rational real number?
Answer and explanation
Correct answer: 0.272727...
A rational number has a decimal expansion that terminates or repeats periodically. In option B, 0.272727… contains the repeating block 27, so it is rational. Let x = 0.272727…. Multiplying by 100 gives 100x = 27.272727…. Subtracting x from this equation gives 99x = 27, so x = 27/99 = 3/11. This is a ratio of integers, and therefore it is a rational real number. Option A is described as non-repeating and infinite, which is the characteristic form of an irrational decimal. √10 is irrational because 10 is not a perfect square, and π is also irrational. Thus only option B satisfies the stated condition.
Frequently asked questions
What is the correct answer to this question?
0.272727...
Why is this the correct answer?
A rational number has a decimal expansion that terminates or repeats periodically. In option B, 0.272727… contains the repeating block 27, so it is rational. Let x = 0.272727…. Multiplying by 100 gives 100x = 27.272727…. Subtracting x from this equation gives 99x = 27, so x = 27/99 = 3/11. This is a ratio of integers, and therefore it is a rational real number. Option A is described as non-repeating and infinite, which is the characteristic form of an irrational decimal. √10 is irrational because 10 is not a perfect square, and π is also irrational. Thus only option B satisfies the stated condition.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Decimal representation.
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