What type of number is (0.121212\ldots)?
Answer and explanation
Correct answer: Rational number
The block 12 repeats continuously, so 0.121212... is a recurring decimal. Every recurring decimal can be written in the form \(\frac{p}{q}\); in fact, \(0.121212... = \frac{12}{99} = \frac{4}{33}\). Therefore, it is a rational number. Irrational numbers have non-terminating, non-recurring decimal expansions. Exam tip: terminating or recurring decimals are always rational.
Frequently asked questions
What is the correct answer to this question?
Rational number
Why is this the correct answer?
The block 12 repeats continuously, so 0.121212... is a recurring decimal. Every recurring decimal can be written in the form \(\frac{p}{q}\); in fact, \(0.121212... = \frac{12}{99} = \frac{4}{33}\). Therefore, it is a rational number. Irrational numbers have non-terminating, non-recurring decimal expansions. Exam tip: terminating or recurring decimals are always rational.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Irrational numbers.
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