Which statement is correct about the number 0.2020020002...?
Answer and explanation
Correct answer: It is an irrational number
The digit '2' appears at positions 1, 3, 6, 10, ... which are triangular numbers with general term \(T_n=\tfrac{n(n+1)}{2}\). The gaps between successive '2's increase, so there is no fixed repeating block (period). Any rational number's decimal expansion is either terminating or eventually periodic; this decimal is neither, therefore it is irrational. Exam tip: to test rationality, check whether the decimal eventually repeats or terminates — if not, it is irrational.
Frequently asked questions
What is the correct answer to this question?
It is an irrational number
Why is this the correct answer?
The digit '2' appears at positions 1, 3, 6, 10, ... which are triangular numbers with general term \(T_n=\tfrac{n(n+1)}{2}\). The gaps between successive '2's increase, so there is no fixed repeating block (period). Any rational number's decimal expansion is either terminating or eventually periodic; this decimal is neither, therefore it is irrational. Exam tip: to test rationality, check whether the decimal eventually repeats or terminates — if not, it is irrational.
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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