Reena says, “Every non-terminating decimal is irrational.” What is the error in her statement?
Answer and explanation
Correct answer: Non-terminating recurring decimals, such as \(0.333...\), are rational.
Reena ignores the difference between non-terminating and recurring decimals. \(0.333...=\frac13\), so it is rational. Only non-terminating, non-recurring decimals are irrational. In exams, check whether digits repeat.
Frequently asked questions
What is the correct answer to this question?
Non-terminating recurring decimals, such as \(0.333...\), are rational.
Why is this the correct answer?
Reena ignores the difference between non-terminating and recurring decimals. \(0.333...=\frac13\), so it is rational. Only non-terminating, non-recurring decimals are irrational. In exams, check whether digits repeat.
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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