What type of number is \(2.\overline{18}\)?
Answer and explanation
Correct answer: Rational number
The decimal is repeating ('18' repeats), so it must be rational because repeating decimals can be written as fractions. For example, let \(x=2.\overline{18}\). Then \(100x=218.\overline{18}\), subtracting gives \(99x=216\), so \(x=\dfrac{216}{99}=\dfrac{24}{11}\). Thus the number is rational. Option B (irrational) is wrong because irrational numbers have non‑repeating, non‑terminating decimals; here the decimal repeats. Options C and D are also incorrect: the number is real (not non‑real) and it is not an integer. Exam tip: convert repeating decimals to fractions by multiplying by an appropriate power of 10 equal to the repeating block length and subtracting.
Frequently asked questions
What is the correct answer to this question?
Rational number
Why is this the correct answer?
The decimal is repeating ('18' repeats), so it must be rational because repeating decimals can be written as fractions. For example, let \(x=2.\overline{18}\). Then \(100x=218.\overline{18}\), subtracting gives \(99x=216\), so \(x=\dfrac{216}{99}=\dfrac{24}{11}\). Thus the number is rational. Option B (irrational) is wrong because irrational numbers have non‑repeating, non‑terminating decimals; here the decimal repeats. Options C and D are also incorrect: the number is real (not non‑real) and it is not an integer. Exam tip: convert repeating decimals to fractions by multiplying by an appropriate power of 10 equal to the repeating block length and subtracting.
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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