Which of the following is a non-terminating but rational decimal?
Answer and explanation
Correct answer: \(0.\overline{12}\)
\(0.\overline{12}\) is a non-terminating recurring decimal; every recurring decimal is rational because it can be expressed as a fraction. For example \(0.\overline{12}=\frac{12}{99}=\frac{4}{33}\), so it is rational and non-terminating. Option B (\(0.875\)) is rational but terminating (\(0.875=\frac{875}{1000}=\frac{7}{8}\)), so it does not meet the "non-terminating" condition. Options C (\(\sqrt{12}=2\sqrt{3}\)) and D (\(\pi\)) are irrational. Exam tip: convert recurring decimals to fractions using 9, 99, 999... under the recurring block to quickly test rationality.
Frequently asked questions
What is the correct answer to this question?
\(0.\overline{12}\)
Why is this the correct answer?
\(0.\overline{12}\) is a non-terminating recurring decimal; every recurring decimal is rational because it can be expressed as a fraction. For example \(0.\overline{12}=\frac{12}{99}=\frac{4}{33}\), so it is rational and non-terminating. Option B (\(0.875\)) is rational but terminating (\(0.875=\frac{875}{1000}=\frac{7}{8}\)), so it does not meet the "non-terminating" condition. Options C (\(\sqrt{12}=2\sqrt{3}\)) and D (\(\pi\)) are irrational. Exam tip: convert recurring decimals to fractions using 9, 99, 999... under the recurring block to quickly test rationality.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.
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