A student claims that the number 0.101001000100001... is rational because it contains only the digits 0 and 1. What is the correct evaluation of this claim?
Answer and explanation
Correct answer: This number is irrational because its decimal expansion is non-terminating and non-repeating.
The number of zeros between successive 1s is 1, 2, 3, 4, ..., so no fixed repeating block occurs. A rational number has a terminating or recurring decimal expansion. Exam tip: check repetition, not merely the digits used.
Frequently asked questions
What is the correct answer to this question?
This number is irrational because its decimal expansion is non-terminating and non-repeating.
Why is this the correct answer?
The number of zeros between successive 1s is 1, 2, 3, 4, ..., so no fixed repeating block occurs. A rational number has a terminating or recurring decimal expansion. Exam tip: check repetition, not merely the digits used.
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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