What type of number is 0.2727727772… on the number line? Here, the number of 7s following each 2 in the decimal expansion keeps increasing.
Answer and explanation
Correct answer: Irrational number
The decimal expansion is non-terminating and non-repeating because the number of 7s after each 2 keeps increasing. Therefore, it cannot be expressed in the form p/q and is irrational. A rational number has a terminating or recurring decimal expansion, so option B is incorrect. Exam tip: a non-terminating, non-repeating decimal is irrational.
Frequently asked questions
What is the correct answer to this question?
Irrational number
Why is this the correct answer?
The decimal expansion is non-terminating and non-repeating because the number of 7s after each 2 keeps increasing. Therefore, it cannot be expressed in the form p/q and is irrational. A rational number has a terminating or recurring decimal expansion, so option B is incorrect. Exam tip: a non-terminating, non-repeating decimal is irrational.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Representing real numbers on the number line.
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