Which statement is correct about the decimal number 3.010010001...?
Answer and explanation
Correct answer: It is an irrational number
In 3.010010001... the number of zeros between successive 1s increases each time (1, 2, 3, ...). Thus there is no fixed repeating block — after any chosen block length the pattern does not repeat. A rational number’s decimal expansion is either terminating or eventually periodic (repeating). Since this decimal is neither terminating nor periodic, it is irrational. The closest distractor C (a repeating decimal) is incorrect because a repeating decimal requires a fixed period of digits repeating indefinitely, which this number does not have. Exam tip: check whether a decimal has a fixed repeating block or terminates; if neither holds and the pattern keeps changing (like increasing zero runs), the number is irrational.
Frequently asked questions
What is the correct answer to this question?
It is an irrational number
Why is this the correct answer?
In 3.010010001... the number of zeros between successive 1s increases each time (1, 2, 3, ...). Thus there is no fixed repeating block — after any chosen block length the pattern does not repeat. A rational number’s decimal expansion is either terminating or eventually periodic (repeating). Since this decimal is neither terminating nor periodic, it is irrational. The closest distractor C (a repeating decimal) is incorrect because a repeating decimal requires a fixed period of digits repeating indefinitely, which this number does not have. Exam tip: check whether a decimal has a fixed repeating block or terminates; if neither holds and the pattern keeps changing (like increasing zero runs), the number 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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