Reena says that \(0.101001000100001\ldots\) is rational because it contains only the digits 0 and 1. Which conclusion correctly identifies the error in her statement?
Answer and explanation
Correct answer: It is irrational because the groups of zeros keep increasing and no repeating decimal block is formed.
A rational number has a terminating or recurring decimal expansion. Here the zeros between 1s occur in groups of 1, 2, 3, 4, ... so no fixed repeating block exists. Exam tip: judge by repetition, not merely by the digits used.
Frequently asked questions
What is the correct answer to this question?
It is irrational because the groups of zeros keep increasing and no repeating decimal block is formed.
Why is this the correct answer?
A rational number has a terminating or recurring decimal expansion. Here the zeros between 1s occur in groups of 1, 2, 3, 4, ... so no fixed repeating block exists. Exam tip: judge by repetition, not merely by the digits used.
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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