In the number \(2.\overline{3}\), the digit 3 repeats indefinitely. What type of number is it?
Answer and explanation
Correct answer: Rational real number
A repeating decimal is always rational because it can be expressed as the ratio of two integers. Here, \(2.\overline{3}=2.333\ldots=\frac{7}{3}\), so it is a rational real number. Irrational decimals are non-terminating and non-repeating. Exam tip: identify a repeating decimal as rational and a non-terminating, non-repeating decimal as irrational.
Frequently asked questions
What is the correct answer to this question?
Rational real number
Why is this the correct answer?
A repeating decimal is always rational because it can be expressed as the ratio of two integers. Here, \(2.\overline{3}=2.333\ldots=\frac{7}{3}\), so it is a rational real number. Irrational decimals are non-terminating and non-repeating. Exam tip: identify a repeating decimal as rational and a non-terminating, non-repeating decimal as irrational.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Rational numbers.
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